Quantum key distribution system and method

Abstract

A continuous-variable Quantum Key Distribution system is provided, comprising a transmitter and a receiver. The receiver comprises a detection part and a lossy optical element arranged between the transmitter and the detection part. The transmitter modulates a quantum signal and sends it to the receiver through a quantum channel. The lossy optical element is configured to: distribute N input modulated quantum signals into M output modulated quantum signals, with N, M ≥ 1, wherein one of the N input signals is associated to the transmitter and the other N-1 signals are vacuum signals; and provide to the detection part one of the M output modulated quantum signals. The receiver detects, with the detection part, one or more quadrature components of the one modulated quantum signal, and performs a post-processing procedure with the transmitter based on the detected quadrature component(s) and an amount of optical loss of the lossy optical element.

Description

[0001] QUANTUM KEY DISTRIBUTION SYSTEM AND METHOD

[0002] TECHNICAL FIELD

[0003] The present disclosure relates to the field of Quantum Key Distribution (QKD). The disclosure provides a continuous- variable (CV) QKD system for increasing the range of the CV-QKD system, and a related method. The disclosure also relates to a computer program to perform the method.

[0004] BACKGROUND QKD systems implement QKD protocols for generating secret keys between at least two distant parties based on quantum physics. The generated keys are information-theoretically secure, in contrast to computational security offered by conventional cryptographic methods.

[0005] There are two main types of QKD protocols adopted in practical QKD systems: discrete-variable (DV) based and CV based. In DV-QKD, the secure bits are derived from information carried in single photons. In CV-QKD, the secure bits are derived from information carried in the quadratures of the quantized electromagnetic wave. DV-QKD and CV-QKD systems rely on different detection technologies for implementation.

[0006] DV-QKD has the disadvantages of requiring specialized single-photon detectors (as opposed to telecom detectors used in CV-QKD) and a separate synchronization channel, which may occupy a different wavelength or a different fiber, while DV-QKD can achieve longer distances.

[0007] The distance of QKD systems is limited by a number of factors that include, for example, the system noise and the channel loss. Therefore, QKD systems often produce keys only up to some distances, i.e., the key range or reach, which are sometimes short for practical purposes. Although conventional QKD systems, which are usually based on fiber optics, have demonstrated the key rate may reach up to 100 km, the key rate may become zero beyond a certain limit.

[0008] Conventional QKD post-processing protocols, in particular the parameter estimation and the privacy amplification steps, consider the online statistics between Alice's transmitted data and Bob's measured data in order to estimate the information leaked to an eavesdropper (or Eve) and to compress an intermediate key to the final secret key. However, it is possible that loss exists naturally in the receiver or that the system designer purposely introduce loss in the receiver. Such a loss in the receiver side, unavoidably, also has an impact on the key reach.

[0009] SUMMARY

[0010] In view of the above, this disclosure aims to improve the conventional devices and methods for increasing the reach in QKD systems. An objective is to provide a device and a method that takes into account the loss existing, either artificially or inherently, in the receiver. Another objective is to provide a way to favorably use the loss of the receiver to perform a parameter estimation step based on QKD data and a privacy amplification step on the QKD data to increase the key rate.

[0011] These and other objectives are achieved by the solutions provided in the independent claims. Advantageous implementations are further defined in the dependent claims.

[0012] A first aspect of the disclosure provides a CV-QKD system comprising a transmitter and a receiver. The receiver comprises a detection part and a lossy optical element, the lossy optical element being arranged between the transmitter and the detection part. The transmitter is configured to: modulate a quantum signal according to a discrete or continuous distribution in phase and amplitude, and send to the receiver the modulated quantum signal through a quantum channel. The lossy optical elementis configured to: distribute N input modulated quantum signals into M output modulated quantum signals, wherein N > 1 and M > 1, wherein one of the N input modulated quantum signals is associated to the transmitter and the other N-l input modulated quantum signals different than the one associated to the transmitter are vacuum signals, and wherein each of the M output modulated quantum signals comprises a fraction of the one input modulated quantum signal associated to the transmitter; and provide, to the detection part, one of the M output modulated quantum signals; wherein the lossy optical element is arranged in a location in the receiver that is inaccessible to an eavesdropper. The receiver is configured to: detect, with the detection part, one or more quadrature components of the one modulated quantum signal received from the lossy optical element; and perform a post-processing procedure with the transmitter to generate a final secret key between the transmitter and the receiver based on the detected one or more quadrature components of the one modulated quantum signal and an amount of optical loss of the lossy optical element.

[0013] By incorporating the lossy optical element in the receiver side, the inherent loss existing naturally in the receiver or an artificial loss introduced in the receiver by the QKD system designer, is implemented. Furthermore, the lossy optical element according to this disclosure is a trusted source of loss. In this disclosure the term "trusted" refers to an element or information that is not accessible to the eavesdropper or that is not leaked to the eavesdropper. Thus, the trusted loss implemented by the lossy optical element that is arranged between the transmitter and the detectors of the receiver (i.e., between the optical channel and the receiver) can become advantageous to Alice and Bob by increasing the key rate when the amount of the loss associated to such a lossy optical element is appropriately introduced in the QKD post-processing, in particular in the parameter estimation and in the privacy amplification steps.

[0014] In an implementation form of the first aspect, the lossy optical element is configured to maintain inaccessible to the eavesdropper the other of the M output modulated quantum signals different than the one modulated quantum signal provided to the detection part. The other of the M output modulated quantum signals of the lossy optical element that are not provided to the detection part may be referred to as unused output light or unused output signals. By keeping secure not only the one output modulated signal but also the unused output signals, the loss associated to receiver is assumed to be dissipated or absorbed in a security premise.

[0015] In an implementation form of the first aspect, the lossy optical element comprises a plurality of N x M ports, each of the N ports being an input port and each of the M ports being an output port.

[0016] In an implementation form of the first aspect, the lossy optical element comprises, or may be, a beam splitter, a polarizing beam splitter, an optical coupler, or a variable optical attenuator (VOA).

[0017] In an implementation form of the first aspect, the receiver further comprises a polarizing beam splitter, the polarizing beam splitter being arranged between the lossy optical element and the detection part; and wherein the polarizing beam splitter is configured to: divide the one modulated quantum signal associated to the transmitter received from the lossy optical element into a first modulated quantum signal having a first polarization and a second modulated quantum signal having a second polarization, the first polarization and the second polarization being different from each other; and provide each of the first modulated quantum signal and the second modulated quantum signal to the detection part. This provides the advantage that two polarizations can be processed by the CV-QKD system in the generation of the final key with enhanced reach.

[0018] In an implementation form of the first aspect, the receiver further comprises a polarizing beam splitter, other lossy optical element and other detection part. The polarizing beam splitter is arranged between the transmitter and both the lossy optical element and the other lossy optical element, and is configured to: divide the modulated quantum signal associated to the transmitter into a first modulated quantum signal having a first polarization and a second modulated quantum signal having asecond polarization, the first polarization and the second polarization being different from each other; and provide the first modulated quantum signal to the lossy optical element and provide the second modulated quantum signal to the other lossy optical element. This provides the advantage that two polarizations can be processed by the CV-QKD system in the generation of the final key with enhanced reach.

[0019] In an implementation form of the first aspect, when the lossy optical element comprises or is the polarizing beam splitter and the receiver comprises other detection part, the lossy optical element is configured to: distribute the N input modulated quantum signals into the M output modulated quantum signals, wherein a first of the M modulated quantum signals has a first polarization and a second of the M modulated quantum sub-signals has a second polarization, the first polarization and the second polarization being different from each other; and provide the first modulated quantum signal to the detection part, and provide the second modulated quantum signal to the other detection part. This provides the advantage that two polarizations can be processed by the CV-QKD system in the generation of the final key with enhanced reach.

[0020] In an implementation form of the first aspect, the post-processing procedure to generate the final secret key between the transmitter and the receiver comprises: a parameter estimation step that takes into account the amount of optical loss of the lossy optical element, and a privacy amplification step that takes into account the amount of optical loss of the lossy optical element. By incorporating the lossy optical element in the receiver side, the QKD post-processing procedure is also adapted to take into account the loss associated to Bob. Thereby, a security proof is provided.

[0021] In an implementation form of the first aspect, the parameter estimation step that takes into account the amount of optical loss of the lossy optical element, comprises: the receiver is configured to determine, with the transmitter, an amount of noise and an amount of loss introduced by the quantum channel to the modulated quantum signal sent by the transmitter before it reaches the receiver by using the amount of optical loss of the lossy optical element, wherein an optical loss of the lossy optical element is inaccessible to the eavesdropper.

[0022] In an implementation form of the first aspect, the privacy amplification step that takes into account the amount of optical loss of the lossy optical element, comprises: the receiver is configured to perform, with the transmitter, hashing on an error corrected key to obtain the final secret key using a compression ratio calculated by taking into account the amount of the optical loss of the lossy optical element and by taking into account the other of the M output modulated quantum signals different than the one modulated quantum signal provided to the detection part and that are inaccessible to the eavesdropper. Even if the amount of loss of the optical element may be known by Eve, the one or more signals "lost" by Alice and / or Bob, i.e., the unused output signals of the lossy optical element, are kept inaccessible to Eve. That is, both the loss of the lossy element and the amount of said loss are inaccessible to Eve.

[0023] Further, the CV-QKD system may carry out the aforementioned parameter estimation step during QKD periods (as part of the QKD post-processing procedure) that computes (or bounds) a mutual information quantity between a system formed by Eve and a system formed by Alice and Bob's key data, which may be non-zero due to and attack from Eve, by assigning the amount of the trusted loss of the lossy optical element to Bob, or by assigning an amount of untrusted loss to Eve.

[0024] The calculation uses the non-orthogonality of the transmitted quantum states (i.e., the modulated quantum signal sent by the transmitter) and statistics resulting from the one or more quantum measurements (detection) performed by the receiver, which cannot be represented as one single projection onto orthogonal states. For example, a quantum covariance matrix between Bob and Eve taking into account the aforementioned constraints may be constructed and quantum mutual information values may be computed from the quantum covariance matrix.In another example, in a correlation-based approach, classical correlations of the measurement results performed by the receiver may be used to derive virtual correlations on a region (point) located before the lossy optical element. These correlations may then be used to model the trusted loss at Bob as introduced by the lossy optical element. The virtual correlations may then be used to construct a quantum covariance matrix describing expectation values related to the quadratures of Alice, Bob, and / or Eve. Further, the CV-QKD system may carry out the privacy amplification step during QKD periods that may compress error-free strings according to a ratio given by the parameter estimation step described above.

[0025] In an implementation form of the first aspect, the post-processing procedure further comprises one or more of: a sifting step, a symbol mapping step, and an information reconciliation step.

[0026] In an implementation form of the first aspect, the CV-QKD system further comprises a calibrator and, before the transmitter modulates the quantum signal, the calibrator is configured to perform a calibration process for the lossy optical element to determine its amount of optical loss. The calibration procedure may be performed during non-QKD periods, i.e., using non-QKD signals / data to quantify the amount of trusted loss either inherent or artificial associated to the receiver, wherein said loss is not leaked to Eve (i.e., it may be dissipated / absorbed in a security premise). After the calibration procedure is performed, the (calibrated) amount of (trusted) optical loss of the lossy optical element is then made available for the QKD post-processing procedure. That is, in this disclosure, the amount of optical loss that is taken into account in the QKD post-processing mentioned above, refers to the value obtained with the calibration process.

[0027] In an implementation form of the first aspect, the calibration process for the lossy optical element to determine its amount of optical loss comprises: the calibrator is configured to provide, to the lossy optical element, input light having an input power, and detect an output power provided by the lossy optical element; determine the value of the optical loss based on a ratio of the output power to the input power; and provide, to the receiver, the determined value of the optical loss of the lossy optical element. Such a calibration process may be performed only once in the lifetime of the CV-QKD system. Alternatively, the calibration process can be performed at the beginning of every QKD phase. In this case, each QKD phase uses an updated value of the amount of loss of the lossy optical element.

[0028] A second aspect of the disclosure provides a method for a CV-QKD system. The CV-QKD system comprises a transmitter and a receiver, the receiver comprises a detection part and a lossy optical element, and the lossy optical element is arranged between the transmitter and the detection part. The method comprises the following steps: modulating, with the transmitter, a quantum signal according to a discrete or continuous distribution in phase and amplitude; sending to the receiver, with the transmitter, the modulated quantum signal through a quantum channel; distributing, with the lossy optical element, N input modulated quantum signals into M output modulated quantum signals, wherein N > 1 and M > 1, wherein one of the N input modulated quantum signals is associated to the transmitter and the other N-l input modulated quantum signals different than the one associated to the transmitter are vacuum signals, and wherein each of the M output modulated quantum signals comprises a fraction of the one input modulated quantum signal associated to the transmitter; providing to the detection part, with the lossy optical element, one of the M output modulated quantum signals, wherein the lossy optical element is arranged in a location in the receiver that is inaccessible to an eavesdropper; detecting, with the detection part of the receiver, one or more quadrature components of the one modulated quantum signal received from the lossy optical element; and performing, with the receiver, a post-processing procedure with the transmitter to generate a final secret key between the transmitter and the receiver based on the detected one or more quadrature components of the one modulated quantum signal and an amount of optical loss of the lossy optical element.In an implementation form of the second aspect, the method further comprises maintaining, with the lossy optical element, inaccessible to the eavesdropper the other of the M output modulated quantum signals different than the one modulated quantum signal provided to the detection part.

[0029] In an implementation form of the second aspect, the lossy optical element comprises a plurality of N x M ports, each of the N ports being an input port and each of the M ports being an output port.

[0030] In an implementation form of the second aspect, the lossy optical element comprises, or may be, a beam splitter, a polarizing beam splitter, an optical coupler, or a VOA.

[0031] In an implementation form of the second aspect, the receiver further comprises a polarizing beam splitter, the polarizing beam splitter being arranged between the lossy optical element and the detection part, and the method further comprises: dividing, with the polarizing beam splitter, the one modulated quantum signal associated to the transmitter received from the lossy optical element into a first modulated quantum signal having a first polarization and a second modulated quantum signal having a second polarization, the first polarization and the second polarization being different from each other; and providing, with the polarizing beam splitter, each of the first modulated quantum signal and the second modulated quantum signal to the detection part.

[0032] In an implementation form of the second aspect, the receiver further comprises a polarizing beam splitter, other lossy optical element and other detection part. The polarizing beam splitter is arranged between the transmitter and both the lossy optical element and the other lossy optical element, and the method further comprises: dividing, with the polarizing beam splitter, the modulated quantum signal associated to the transmitter into a first modulated quantum signal having a first polarization and a second modulated quantum signal having a second polarization, the first polarization and the second polarization being different from each other; and providing, with the polarizing beam splitter, the first modulated quantum signal to the lossy optical element and provide the second modulated quantum signal to the other lossy optical element.

[0033] In an implementation form of the second aspect, when the lossy optical element comprises or is the polarizing beam splitter, the receiver comprises other detection part and the method further comprises: distributing, with the lossy optical element, the N input modulated quantum signals into the M output modulated quantum signals, wherein a first of the M modulated quantum signals has a first polarization and a second of the M modulated quantum sub-signals has a second polarization, the first polarization and the second polarization being different from each other; and providing, with the lossy optical element, the first modulated quantum signal to the detection part, and providing, with the lossy optical element, the second modulated quantum signal to the other detection part.

[0034] In an implementation form of the second aspect, the post-processing procedure to generate the final secret key between the transmitter and the receiver comprises: a parameter estimation step that takes into account the amount of optical loss of the lossy optical element, and a privacy amplification step that takes into account the amount of optical loss of the lossy optical element.

[0035] In an implementation form of the second aspect, the parameter estimation step that takes into account the amount of optical loss of the lossy optical element, comprises: determining, with the receiver and with the transmitter, an amount of noise and an amount of loss introduced by the quantum channel to the modulated quantum signal sent by the transmitter before it reaches the receiver by using the amount of optical loss of the lossy optical element, wherein an optical loss of the lossy optical element is inaccessible to the eavesdropper.In an implementation form of the second aspect, the privacy amplification step that takes into account the amount of optical loss of the lossy optical element, comprises: performing, with the receiver and with the transmitter, hashing on an error corrected key to obtain the final secret key using a compression ratio calculated by taking into account the amount of the optical loss of the lossy optical element and by taking into account the other of the M output modulated quantum signals different than the one modulated quantum signal provided to the detection part and that are inaccessible to the eavesdropper.

[0036] In an implementation form of the second aspect, the post-processing procedure further comprises one or more of: a sifting step, a symbol mapping step, and an information reconciliation step.

[0037] In an implementation form of the second aspect, the CV-QKD system further comprises a calibrator and, before modulating, with the transmitter, the quantum signal, the method further comprises performing, with the calibrator, a calibration process for the lossy optical element to determine its amount of optical loss.

[0038] In an implementation form of the second aspect, wherein the performing, with the calibrator, a calibration process for the lossy optical element to determine its amount of optical loss, comprises: providing, with the calibrator to the lossy optical element, input light having an input power, and detecting an output power provided by the lossy optical element; determining, with the calibrator, the value of the optical loss based on a ratio of the output power to the input power; and providing, with the calibrator to the receiver, the determined value of the optical loss of the lossy optical element.

[0039] The method according to the second aspect its implementation forms provide the same advantages and effects as described above for the CV-QKD system of the first aspect and its respective implementation forms.

[0040] A third aspect of the disclosure provides a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps performed by the receiver and / or the transmitter according to the method of the second aspect.

[0041] Additionally or alternatively, the computer program comprises instructions which, when the program is executed by a computer, cause the computer to carry out the steps performed by the lossy optical element according to the method of the second aspect.

[0042] Additionally or alternatively, the computer program comprises instructions which, when the program is executed by a computer, cause the computer to carry out the steps performed by the detection part according to the method of the second aspect.

[0043] The computer program according to the third aspect provides the same advantages and effects as described above for the receiver and / or the transmitter and / or the lossy optical element and / or the detection part according to the method of the second aspect and their respective implementation forms.

[0044] The main advantages of the solutions according to this disclosure can be summarized as follows:

[0045] • An inherent or artificial loss of the receiver is implemented by introducing a trusted lossy optical element in the receiver, which is arranged between the transmitter and the detection components of the receiver. The lossy optical element, the loss added by lossy optical element, the amount of said optical loss, and the quantum signals that are distributed by lossy optical element, are all inaccessible to Eve.

[0046] • The amount of loss of the lossy optical element is be appropriately calibrated and then used by the QKD post-processing, in particular in the parameter estimation and privacy amplification steps, thereby providing with a novel security proof.

[0047] • The trusted loss introduced by the lossy optical element according to the solutions of this disclosure is proven to be beneficial as it increases the reach of the QKD system.It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

[0048] BRIEF DESCRIPTION OF DRAWINGS

[0049] The above described aspects and implementation forms of the present disclosure will be explained in the following description of more specific embodiments in relation to the enclosed drawings, in which

[0050] FIG. 1 shows a schematic view of a CV-QKD system where a trusted lossy element is considered, according to according to this disclosure;

[0051] FIG. 2 shows a schematic view of an example for an implementation of a CV-QKD system according to according to this disclosure;

[0052] FIG. 3 shows a schematic view of an example for an implementation of a CV-QKD system according to according to this disclosure;

[0053] FIG. 4 shows a schematic view of a CV-QKD system according to according to this disclosure;

[0054] FIG. 5 shows a schematic view of a CV-QKD system according to according to this disclosure;

[0055] FIG. 6 shows a schematic view of a CV-QKD system where two different polarizations may be processed, according to this disclosure;

[0056] FIG. 7 shows a schematic view of a CV-QKD system where two different polarizations may be processed, according to this disclosure;

[0057] FIG. 8 shows a schematic view of an example for an implementation of the CV-QKD system according to FIG. 7; FIG. 9 shows a schematic view of a CV-QKD system where two different polarizations may be processed, according to this disclosure;

[0058] FIG. 10 shows a schematic view of a CV-QKD system where two different polarizations may be processed, according to this disclosure;

[0059] FIG. 11 shows a schematic view of an example for an implementation of the CV-QKD system according to FIG. 10; FIG. 12 shows a schematic view of a CV-QKD system where two different polarizations may be processed, according to this disclosure;

[0060] FIG. 13 shows a schematic view of an example for an implementation of the CV-QKD system according FIG. 12; FIG. 14 shows a schematic view of a CV-QKD system according to this disclosure;

[0061] FIG. 15a)-b) schematically depict a calibration process of a CV-QKD system according to this disclosure;

[0062] FIG. 16 shows exemplary results of the reach achieved with a CV-QKD system according to this disclosure; FIG. 17 shows a flowchart of a method for a CV-QKD system according to this disclosure;

[0063] FIG. 18 shows a flowchart of a customary method for performing QKD.

[0064] Same elements shown in the figures are labeled with the same reference sign, and may be implemented likewise. The size of elements in the figures is not to scale and may be different compared to a real-life implementation in order to highlight details of the disclosure.DETAILED DESCRIPTION OF EMBODIMENTS

[0065] FIG. 18 is a flowchart of a conventional QKD protocol, in which a transmitting device 1801 (corresponding to the user Alice) prepares a quantum state selected from a pre-agreed set. The quantum state is then transmitted to a receiving device 1811 (corresponding to the user Bob), in the presence of an eavesdropper 1821 (corresponding to Eve), over a quantum channel.

[0066] Hereinafter in this disclosure, the terms "transmitter device" "transmitter" and " Alice" will be used interchangeably. Likewise, the terms "receiving device", "receiver" and " Bob" will be used interchangeably. Further, the terms "eavesdropping device", "eavesdropper" and " Eve" will be used interchangeably.

[0067] The receiving device 1811 detects the received signal with a detection system that implements a quantum measurement. In DV-QKD, it is often the case that detection in the receiving device 1811 is tuned to a random setting for each received signal and this setting corresponds to the quantum basis of the measurement. Since the setting is randomly chosen, the detected information may be completely uncorrelated with the state that the transmitting device 1801 has sent (when the setting is chosen to be incompatible with Alice's state). These uncorrelated cases are dropped in a sifting step afterwards.

[0068] After transmission of the quantum state, in the form of a modulated quantum signal, the transmitting device 1801 perform QKD post-processing (step S18011 in FIG. 18) and the receiving device 1811 may perform the QKD post-processing (steps S18111 in FIG. 18) on classical computing devices connected by a classical error- free, authenticated, and unjammable channel to transform the raw data into a final secret key. The QKD post-processing (or simply "post-processing") generally comprises a few main steps: parameter estimation, sifting (or basis selection), symbol mapping, information reconciliation, and privacy amplification.

[0069] In the parameter estimation step, Alice 1801 and Bob 1811 estimate the properties of the quantum channel which allow them to infer how much noise and loss there are in the raw key and how much information about the raw key has been leaked to Eve 1821.

[0070] Then, in the sifting (or basis selection) step, which predominately exists in DV-QKD, Alice 1801 and Bob 1811 discard signal pairs where Bob 1811 has used a setting incompatible with Alice's state.

[0071] In the symbol mapping step, which predominately exists in CV-QKD, Alice 1801 and Bob 1811 map the real- valued signal data into bit values (and soft information) for further processing.

[0072] In the information reconciliation step, Alice 1801 and Bob 1811 correct the differences between their keys to arrive at matching keys. Usually only one ofthem performs error correction on one's data to match the other's data. In CV-QKD, Alice 1801 corrects her data to match Bobs' data and this is called reverse reconciliation, whereas forward reconciliation is where Bob 1811 corrects his data to match Alice's.

[0073] Further, in the privacy amplification step, Alice 1801 and Bob 1811 perform a length-shortening operation that is specially designed to remove Eve's 1821 information on the key. After this, Alice 1801 and Bob 1811 should get a final key secure against Eve 1821. These steps are depicted in FIG. 18.

[0074] This disclosure is particularly related to the parameter estimation step and the privacy amplification step when a certain loss in the receiver may be taken into account.

[0075] Further, this disclosure is related to CV-QKD. The solutions and advantages can also be applied to DV-QKD.FIG. 1 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure. The CV-QKD system 1 comprises a transmitter 100 (Alice) and a receiver 110 (Bob) that are in communication with each other through a quantum channel 102. The receiver 110 comprises a detection part 111 and a lossy optical element 112. The lossy optical element 112 is arranged between the transmitter 100 and the detection part 111 of the receiver 110. The lossy optical element 112 is arranged, in particular, in a location in the receiver 110 that is inaccessible to an eavesdropper (Eve). That is, the lossy optical element 112 may be considered to be arranged between the quantum channel 102 and the detection part 111 of the receiver, always being inaccessible to Eve. Thus, the lossy optical element 112 is a trusted element and, accordingly, the loss introduced by the lossy optical element 112 is a trusted loss, and the amount of the optical loss is also a trusted value.

[0076] The CV-QKD system 1 may comprise processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the CV-QKD system 1 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the CV-QKD system 1 to perform, conduct or initiate the operations or methods described herein.

[0077] The transmitter 100 may comprise processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the transmitter 100 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the transmitter 100 to perform, conduct or initiate the operations or methods described herein.

[0078] The receiver 110 may comprise processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the receiver 110 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the receiver 110 to perform, conduct or initiate the operations or methods described herein.

[0079] The lossy optical element 112 may comprise processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the lossy optical element 112 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the lossy optical element 112 to perform, conduct or initiate the operations or methods described herein.The detection part 111 of the receiver 110 may comprise processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the detection part 111 described herein. The processing circuitry may comprise hardware and software. The hardware may comprise analog circuitry or digital circuitry, or both analog and digital circuitry. The digital circuitry may comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. In one embodiment, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory may carry executable program code which, when executed by the one or more processors, causes the detection part 111 to perform, conduct or initiate the operations or methods described herein.

[0080] Referring to FIG. 1, the transmitter 100 is configured to modulate a quantum signal 101 according to a discrete or continuous distribution in phase and amplitude. Then, the transmitter 100 is configured to send to the receiver 110 the modulated quantum signal 101 through the quantum channel 102. The lossy optical element 112 is configured to distribute N input modulated quantum signals 101, 113 into M output modulated quantum signals 114, 115, where N > 1 and M > 1.

[0081] One 101 of the N input modulated quantum signals is associated to the transmitter 100 (that is, one of the N input modulated quantum signals may be the signal 101 modulated and transmitted by Alice 100), and the other N-l input modulated quantum signals 113 different than the one 101 associated to the transmitter 100 are vacuum signals.

[0082] Further, each of the M output modulated quantum signals 114, 115 comprises a fraction of the one 101 input modulated quantum signal associated to the transmitter 100. That is, each of the M output modulated quantum signals 114, 115 of the lossy optical element 112 may comprise, or may be equal to, 1 / M-th of the one modulated quantum signal 101 associated to the transmitter 100. Then, the lossy optical element 112 is configured to provide, to the detection part 111 of the receiver 110, only one 115 of the M output modulated quantum signals 114, 115.

[0083] Since the lossy optical element 112 is inaccessible to Eve, the lossy optical element 112 may be configured to maintain inaccessible to the eavesdropper all the M output modulated quantum signals 114, 115. That is, the one output modulated quantum signal 115 that is provided by the lossy optical element 112 to the detection part 111 is inaccessible to Eve. Additionally, the other M-l output modulated quantum signals 114 of the lossy optical element are also inaccessible to Eve. The lossy optical element 112 may comprise a plurality ofN xM ports 1121, 1122. Each of the N ports 1121 is, or acts as, an input port that may be configured to receive a respective one of the N input modulated quantum signals 101, 113. Additionally, each of the M ports 1122 is, or acts as, an output port that may be configured to provide a respective one of the M output modulated quantum signals 114, 115.

[0084] The lossy optical element 112 may comprise, or may be, a beam splitter, a polarizing beam splitter, an optical coupler, or a VOA. Then, the receiver 110 is configured to detect, using the detection part 111, one or more quadrature components of the one modulated quantum signal 115 that is received from the lossy optical element 112. Further, the receiver 110 is configured to perform a post-processing procedure with the transmitter 100 to generate a final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more quadrature components of the one modulated quantum signal 115 and based on an amount of optical loss of the lossy optical element 112. That the receiver 110 performs the post-processing procedure with the transmitter 100 means that the receiver 110 and the transmitter 100 process an output of the detection part 111, and generate the secret key 116 between Alice 100 and Bob 110.

[0085] The lossy optical element 112 may implement a loss present in, or related to, the receiver 110. Thus, the optical loss of the lossy optical element 112 and an amount of said optical loss may represent an inherent loss of the receiver 110. Alternatively,the optical loss of the lossy optical element 112 and an amount of said optical loss may represent other source(s) of loss related to the receiver 110, for example a source of loss associated to the typical components of the receiver 110.

[0086] By adding the lossy optical element 112 to the CV-QKD system 1, the trusted loss associated or related to the receiver 110 can become advantageous to Alice 100 and Bob 110 by increasing the key rate. Therefore, the QKD post-processing procedure of the CV-QKD system 1, in particular the parameter estimation step and the privacy amplification step, should be adapted to take into account the trusted loss.

[0087] The amount of optical loss of the lossy optical element 112 may be known by the receiver 110. For example, the amount of optical loss of the lossy optical element 112 may be calibrated by the CV-QKD system 1 (as explained later on in this disclosure), or may be identified or calculated during the manufacture of the CV-QKD system 1, or may be obtained from a data sheet of the lossy optical element 112 and / or from a data sheet of the detection part 111. Once the amount of optical loss is known by the receiver 110, it may be accessible for performing, by the receiver 110 together with the transmitter 100, the post-processing procedure to generate the final secret key 116 between Alice 100 and Bob 110.

[0088] The post-processing procedure to generate the final secret key 116 between the transmitter 100 and the receiver 110 according to this disclosure comprises: a parameter estimation step that takes into account the amount of optical loss of the lossy optical element 112, and a privacy amplification step that also takes into account the amount of optical loss of the lossy optical element 112.

[0089] The parameter estimation step that takes into account said amount of optical loss of the lossy optical element 112 comprises the following: The receiver 110 is configured to determine, together with the transmitter 100, an amount of noise and an amount of loss introduced by the quantum channel 102 to the modulated quantum signal 101 that is sent by the transmitter 100 before it reaches the receiver 110 by using the amount of optical loss of the lossy optical element 112.

[0090] Then, the privacy amplification step that takes into account the amount of optical loss of the lossy optical element 112, comprises: The receiver 110 is configured to perform, together with the transmitter 100, hashing on an error corrected key to obtain the final key 116 using a compression ratio calculated by taking into account the amount of the optical loss of the lossy optical element 112 and by taking into account the other of the M output modulated quantum signals 114 different than the one modulated quantum signal 115 provided to the detection part 111 and that are inaccessible to the eavesdropper.

[0091] In each of the aforementioned parameter estimation and privacy amplification steps, the optical loss of the lossy optical element 112 is also inaccessible to the eavesdropper, as explained above. Further, the post-processing procedure comprises one or more of: a sifting step, a symbol mapping step, and an information reconciliation step.

[0092] Details of the QKD post-processing according to this disclosure are now presented. Assuming that there is no other intrinsic loss or noise in the receiver 110, the only loss is the optical loss of the lossy optical element 112. Then, measurement statistics between the transmitter 100 and the receiver 110 may be collected after the lossy optical element 112. This refers to the fact that the lossy optical element 112 is arranged between the transmitter 100 and the detection part 111 of the receiver 110. Then, it is assumed that the data encompassed in the modulated quantum signal 101 is in a scale where shot noise is normalized to 2. Next, a complex symbol of Alice 100 is denoted by xl + i x2 and complex symbol of Bob's measurement outcome by zl + i z2.

[0093] The measurement outcome mentioned above may be produced inside the detection part 111 of the receiver 110. For example and not as a limitation, it is assumed that the receiver 110 performs, with the detection part 111, a coherent measurement thatmeasures the x and p quadratures, where the x value is represented by a real part of said measurement outcome, and the p value is the imaginary part.

[0094] It is assumed that Alice 100 uses a Gaussian modulation to modulate the transmitted quantum signal 101. Each of xl and x2 is drawn from a Gaussian distribution with mean zero and variance VA. Then, it is assumed a natural case where there is no correlation between the real and imaginary values between Alice and Bob, i.e., E[xl z2] = E[x2 zl] = 0, where E[X] denotes t

[0095]

[0096] he expected value of a random variable X.

[0097] It is also assumed the natural case that the mean of the measurement outcome is zero, i.e. E[zl + i z2] = 0.

[0098] Then, a covariance matrix can be calculated, which takes the form of Equation (1):

[0099] E[xl zl] > - E[xl zl] / >i >T- \ V* * V trusted® Z * V * trusted® Z \

[0100] >. ((£[zl zl] - 2) * Ttrusted+ 1)7 ((£[zl zl] - 2) * ^(1 - Ttrusted)Ttrusted)I I’

[0101] ((£[zl zl] - 2) * (1 - Ttrusted) + 1) / /

[0102] where A = V = VA+ 1, azis the Pauli Z matrix, I is the 2x2 identity matrix, and Ttrustedis the amount of optical loss of the lossy optical element 112 and is assumed to be obtained in the calibration procedure that will be explained later in this

[0103]

[0104] description,

[0105] The covariance matrix may be associated to a virtual quantum state that describes a hypothetical Alice's optical mode, and two Bob's optical modes (which are the M output modulated quantum signals 114, 115, assuming M=2 here). The hypothetical Alice's optical mode may be in one of two optical modes of a quantum entangled state that describes an initial state of the QKD protocol. The other optical mode may be transmitted through the quantum channel 102 as the transmitted quantum signal 101, as in a real situation. Alice's optical mode serves as a theoretical construction that may not directly correspond to a physical optical signal but when a coherent measurement (x and p) is applied to the optical mode, Alice's data (the complex symbol of Alice 100 mentioned above) is generated. Thus, Alice’s optical mode and the coherent measurement together may be viewed as a theoretical equivalent to the generation of Alice’ s data. Overall, the quantum entangled state may be introduced to describe the QKD protocol as a virtual equivalent whose purpose is to facilitate the security analysis.

[0106] Thus, the covariance matrix in Equation (1) is for three systems: Alice's optical mode, Bob's optical mode that corresponds to the transmitted light through the (trusted) lossy optical element 112, and Bob's second optical mode that corresponds to the (unused) reflected light from the (trusted) lossy optical element 112, i.e., the other of the M output modulated quantum signals 114 different than the one 115 that is provided to the detection part 111. The three systems are denoted as 4, Bl, B2.

[0107] Then, it is assumed that symmetry holds: E [xl zl] = E [x2 z2] and E [zl zl] = E [z2 z2]. Thus, the lower triangle part of the covariance matric C in Equation (1) may be understood to be transposed values of the upper triangle part, so that C is a symmetric matrix.Further, C is a quantum covariance matrix for x = \cji, Pi> P2> P2> Pi> Pi \ for the two quadratures of Alice, Bob's system 1 and Bob's system 2 respectively. Then, the quantum covariance matrix can be defined in Equation (2) as:

[0108] C(2

[0109]

[0110] U = |<{4xi, Ax / }) )

[0111] where Ax,- = xt— xt} and {, } is the anti-commutator.

[0112] Eve's information can then be calculated, and the key rate can be calculated as in Equation (3):

[0113] I(E B1) = S(E) -S(E\B1). (3)

[0114] In Equation (3), S( E) is the entropy of Eve before the measurement and S(B|B1) is the conditional entropy of Eve conditioned on Bob's system 1.

[0115] The entropy of Eve before the measurement is computed as S(E) = S(A, B1, B2). which can be directly calculated from the symplectic eigenvalues of C using standard entropy formulas for Gaussian states.

[0116] For the calculation of the conditional entropy S(B| Bl), a conditional covariance matrix for A and B2 after a double-homodyne measurement of Bl is first obtained by standard formulas for Gaussian states as follows: The conditional covariance matrix is defined as in Equation (4):

[0117] a - y( / ? + / )1yT, (4)

[0118] where:

[0119] (5)

[0120] (6)

[0121] (7)

[0122]

[0123] I is the 2x2 identity matrix, C is from Equation (1 ), and Ctj is the element of C at row i and column j.

[0124] Then, S(B|B1) is computed asS(B|Bl) = S(A, B2|B1). which is directly calculated from the symplectic eigenvalues of the aforementioned conditional covariance matrix using standard entropy formulas for Gaussian states.

[0125] Then, the final key 116 is calculated and is given in Equation (8):

[0126] I(A B1) - I(E B1),where I (: Bl) is the mutual information between Alice's system and Bob's system Bl.

[0127] Alternatively, the covariance matrix may be calculated by directly involving Eve and may be used to compute Eve's information and to subsequently compute the key rate. A standard approach is to assume that Eve launches an entangling cloner attack with a certain excess noise variance and a certain channel loss value. In this way, the covariance matrix involving Eve may be formed by evolving an initial covariance of Alice 100 according to the dynamics of the entangling cloner attack. In order to do that, the excess noise variance (as a parameter of the entangling cloner attack) needs to be inferred.

[0128] The first method mentioned above relies on having the data correlations between Alice 100 and Bob 110 estimated. The second method relies on having the excess noise variance attributed to Eve estimated. Both methods provide the advantage of determining the final key 116 with an enhanced reach by taking into account the loss, either inherent or artificial, attributed to Bob.

[0129] In other words, in the CV-QKD system 1 according to FIG. 1, the lossy optical element 112 that implements the inherent / artificial loss associated to the receiver 110 and, notably, has a beneficial impact on the CV-QKD system 1 resulting in an enhanced key reach, as shown in the simulation results according to FIG. 16.

[0130] FIG. 2 is a schematic view of an example implementation of a CV-QKD system 1 according to this disclosure, which builds on the CV-QKD system 1 according to FIG. 1.

[0131] In the CV-QKD system 1 according to FIG. 2, Alice 100 may perform a continuous Gaussian modulation to modulate the quantum signal 101. The transmitter 100 may comprise different components as e.g., a strong laser (for example a continuous wave (CW) depicted in FIG. 2), an amplitude and phase modulation block (depicted as IQ in FIG. 2) and an attenuator modulator (depicted as Att in FIG. 2).

[0132] The modulated optical signal may be attenuated in the Att to a weak signal so that the quantum effects become dominant. Then, the attenuated modulated quantum signal 101 may be transmitted by Alice 100 to Bob 110 through the quantum channel 102. Alice 100 may then transmit the modulated quantum signal 101 to Bob 110 through the quantum channel 102. An eavesdropper may perform an attack on the modulated quantum signal 101 before it reaches Bob 110.

[0133] The receiver 110 may comprise the lossy optical element 112, and said lossy optical element 112 may comprise, or may be, a coupler or an optical beam splitter. In the exemplary embodiment, the lossy optical element 112 may implement an artificial trusted loss added to the receiver 110.

[0134] The lossy optical element 112 may receive the modulated quantum signal 101 sent by Alice and other N-l vacuum signals, and may distribute them into M output modulated quantum signals. Further, the lossy optical element 112 may provide the one of the M output modulated quantum signals 115 to the detection part 111. For the sake of clarity and without limitation, only the one input modulated quantum signal 101 and the one output modulated quantum signal 115 are shown in FIG. 2.

[0135] The detection part 111 of the receiver may comprise one or more detection components, as schematically depicted in FIG. 2. For example, a strong laser (depicted as the CW laser in FIG. 2) may be used as a local oscillator (LO) with optimal power to reduce noises. The one quantum signal 115 received from the lossy optical element 112 and the LO may interfere to reproduce a signal that may be processed by a digital signal processor (DSP in FIG. 2) to reconstruct the original signal 115, for exampleusing also an analog-to-digital convertor (ADC in FIG. 2). Further, training for phase error recovery may be done by the DSP. The detection part 111 according to FIG. 2 and its components are only an example and do not limit the present disclosure.

[0136] The detection part 111 may be used by the receiver 110 to detect the one or more quadratures (or quadrature components) of the one modulated quantum signal 115 received from the lossy optical element 112 and that is associated to Alice's signal 101.

[0137] Then, Bob 110 may perform, together with Alice 100, the QKD post-processing, e.g. the parameter estimation and privacy amplification steps that take into account the amount of optical loss of the lossy optical element 112, to generate the key 116. The QKD post-processing according to this disclosure has been explained above, and the details are not repeated again here.

[0138] The example depicted in FIG. 2 does not limit the present disclosure.

[0139] FIG. 3 schematically depicts an example for an implementation of a CV-QKD system 1 according to this disclosure, which builds on the CV-QKD system 1 according to FIG. 1. In the CV-QKD system 1 according to FIG. 3, Alice 100 may perform a discrete modulation of the quantum signal 101. The transmitter may comprise different components as e.g., a CW laser, a phase modulator block (PM in FIG. 3) and an attenuator modulator (Att in FIG. 3). In this example, Alice 100 may randomly selected symbols and further modulated them onto a carrier. Possible constellations include Quadrature Phase Shift Keying (QPSK), {TT / 4, 3TT / 4, 5TT / 4, 7TT / 4} and Gaussian distributions centered at the origin.

[0140] The modulated optical signal may be attenuated to a weak signal so that the quantum effects become dominant. Then, the attenuated modulated quantum signal may be transmitted by Alice 100 to Bob 110 through the quantum channel 102.

[0141] An eavesdropper may perform an attack on the modulated quantum signal 101 before it reaches Bob 110. Bob 110 may comprise the lossy optical element 112, and it may comprise, or may be, a coupler or an optical beam splitter. Similar to the exemplary implementation according to FIG 2, in the exemplary implementation according to FIG. 3, the lossy optical element 112 may implement an artificial trusted loss added to the receiver 110. The lossy optical element 112 may receive the modulated quantum signal 101 sent by Alice and the other N-l vacuum signals (not shown), and may distribute them into the M output modulated quantum signals (not all them are shown) and may provide the one of the M output modulated quantum signals 115 to the detection part 110.

[0142] The detection part 111 of the receiver 110 may comprise one or more detection components, similar to those schematically depicted in FIG. 3. These exemplary components have been explained above in the example according to FIG. 2 and are not be repeated again.

[0143] Then, Bob 110 may perform, together with Alice 100, the QKD post-processing, e.g. the parameter estimation and privacy amplification steps, which take into account the amount of optical loss of the lossy optical element 112, to generate the key 116. The QKD post-processing according to this disclosure has been explained above, and the details are not repeated again here.

[0144] FIG. 4 schematically depicts an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds on the CV-QKD system 1 according to FIG. 1. Hereinafter, only the differences between FIG. 4 and FIG. 1 are presented.

[0145] In the CV-QKD system 1 according to FIG. 4, the lossy optical element 112 may comprise, or may be implemented as, a lossy balance detector within the receiver 110. Thus, in this exemplary embodiment, the lossy optical element 112 may implement an intrinsic or inherent loss present in the receiver 110.In this exemplary implementation, the lossy balance detector 112 may receive N input optical signals (not all of them are shown), and one of them may be the modulated quantum signal 101 associated to the transmitter 100. Further, the lossy balance detector 112 may distribute the N input optical signals into M modulated optical signals (not all of them are shown) and may provide the one output modulated quantum signal 115 to the detection part 111. In this exemplary embodiment, the detection part 111 may comprise one or more components except for the lossy balance detector 112. For example, and without limitation, the detection part 111 may comprise a CW laser, an ADC and a DSP.

[0146] Then, the receiver 110 may detect, with the detection part 111, the one or more quadrature components of the one modulated quantum signal 115, and may further perform, with the transmitter 100, the post processing procedure that takes into account the amount of optical loss of the lossy balance detector 112 (i.e., the lossy optical element), as explained above for the CV-QKD system 1 according to FIG. 1. The details are not repeated again.

[0147] FIG. 5 schematically depicts an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds on the CV-QKD system 1 according to FIG. 1. Hereinafter, only the differences between FIG. 5 and FIG. 1 are presented. In the CV-QKD system 1 according to FIG. 5, the lossy optical element 112 comprises, or is, the VOA. The VOA may comprise one input port and one output port that are exposed to a user. The VOA may further comprise one or more virtual (or implicit) input ports and / or one or more virtual (or implicit) output ports, where the terms "virtual" or "implicit" indicate that a respective input or output port are not exposed. Accordingly, the VOA may receive the one input modulated quantum signal 101 associated to the transmitter 100 with the exposed input port and may provide the one output modulated quantum signal 115 to the detection part 111 with the exposed output port.

[0148] In this exemplary embodiment, it is assumed that one or more input vacuum signals may be injected into a corresponding virtual (or implicit) input port, which are not exposed to the user, where the one or more virtual input ports may be effectively implemented by one or more structures such as the side walls of the VOA 112. Thus, the VOA 112 may distribute the input modulated quantum signal 101 and the assumed one or more vacuum signals 114 (not shown) into the M output modulated quantum signals, which include the one output modulated quantum signal 115 provided to the detection part 111, and at least one other output modulated quantum signal that may be assumed to be injected into a respective at least one virtual (or implicit) output port, which are not exposed to the user, where the at least one virtual output port may be effectively implemented by one or more structures such as the side walls of the VOA 112 and may represent dissipation of energy in the structures.

[0149] Then, the receiver 110 may detect, with the detection part 111, the one or more quadrature components of the one modulated quantum signal 115. Further, the receiver 110 may perform the post processing procedure with the transmitter 100 to generate the final secret key 116 based on the detected one or more quadrature components of the one modulated quantum signal 115 and the amount of optical loss of the VOA 112, as explained above. The details are not repeated again here.

[0150] This exemplary embodiment provides the same advantages of the exemplary embodiments according to FIGS. 1 and 4. In addition, the VOA provides a changeable (or controllable) setting that allows setting the amount of optical loss of the VOA 112 at different values. This amount of optical loss, thus, may be chosen / tailored to optimize the key reach. Accordingly, this exemplary embodiment further provides the flexibility to adapt the lossy optical element 112 to different operating situations by adjusting its amount of optical loss.

[0151] For example, an initial amount of optical loss of the VOA (i.e., the lossy element 112) may be determined by performing the calibration procedure that is explained later in this disclosure. Then, the setting of the VOA 112 may be changed to take on theinitial amount of the loss and the post-processing procedure according to this disclosure may be performed to obtain the final key 116 and the key reach.

[0152] This may be done once during deployment time of the CV-QKD system 1, or may be done periodically during the QKD operation. For example, the setting on the VOA 112 may be changed again in another QKD operation to achieve a larger key rate distance, and the process may be repeated until the reach is optimized.

[0153] FIG. 6 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds in the CV-QKD system 1 according to FIG. 1. Hereinafter, only the differences between FIG. 6 and FIG. 1 are presented. In the CV-QKD system 1 according to FIG. 6, the receiver 110 further comprises a polarizing beam splitter 117 that is arranged between the lossy optical element 112 and the detection part 111.

[0154] In this exemplary embodiment, the lossy optical element 112 may provide the one 115 of the M output modulated quantum signals to the detection part 111 via the polarizing beam splitter 117. That is, the lossy optical element 112 may provide the one output modulated quantum signal 115 to the polarizing beam splitter 117. Then, the polarizing beam splitter 117 is configured to divide the at least one modulated quantum signal 115 associated to the transmitter 100 received from the lossy optical element 112 into a first modulated quantum signal 118 having a first polarization and a second modulated quantum signal 119 having a second polarization.

[0155] The first polarization and the second polarization are different from each other. For example and without limitation, the first polarization may be a horizontal polarization and the second polarization may be a vertical polarization. Each of the first modulated quantum signal 118 having the first polarization and the second modulated quantum signal 119 having the second polarization is associated to the modulated quantum signal 101 prepared and transmitted by Alice 100.

[0156] The polarizing beam splitter 117 is further configured to provide each of the first modulated quantum signal 118 and the second modulated quantum signal 119 to the detection part 111.

[0157] Then, the receiver 110 may detect, with the detection part 111, one or more quadrature components of each the first modulated quantum signal 118 having the first polarization and the second modulated quantum signal 119 having the second polarization that are received from the lossy optical element 112 via the polarizing beam splitter 117.

[0158] In other words, the receiver 110 may detect one or more quadrature components of the first modulated quantum signal 118 having the first polarization, and may detect one or more quadrature components of the second modulated quantum signal 119 having the second polarization.

[0159] Then, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate the final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more quadrature components of both the first modulated quantum signal 118 having the first polarization and the second modulated quantum signal 119 having the second polarization, and taking into account the amount of optical loss of the lossy optical element 112.

[0160] The post-processing procedure explained above for the embodiments according to FIG. 1 may be directly extended to perform the parameter estimation and privacy amplification steps considering the one or more quadrature components of both the first and second modulated quantum signals 118, 119, and taking into account the amount of optical loss of the lossy element 112, in order to generate the final key 116, which may comprise information carried by the two polarizations of Alice's signal. The details are not repeated again here.The exemplary embodiment according to FIG. 6 provides the same advantages as the exemplary embodiment according to FIG. 1, whilst allowing the processing of two different polarizations.

[0161] FIG. 7 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds in the CV-QKD system 1 according to FIG. 6. Hereinafter, only the differences between FIG. 7 and FIG. 6 are presented. In the CV-QKD system 1 according to FIG. 7, the receiver 110 may further comprise other detection part 111-2.

[0162] The polarizing beam splitter 117 may then be configured to provide the first modulated quantum signal 118 having the first polarization to the detection part 111, and provide the second modulated quantum signal 119 to the other detection part 111-2.

[0163] The receiver 110 may detect, with the detection part 111, one or more first quadrature components of the first modulated quantum signal 118 having the first polarization. Further, the receiver 110 may detect, with the other detection part 111-2, one or more second quadrature components of the second modulated quantum signal 119 having the second polarization.

[0164] Then, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate the final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more first quadrature components of the first modulated quantum signal 118 having the first polarization. The final secret key 116 may be related to information of Alice's signal that is carried by the first polarization.

[0165] Additionally, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate other final secret key 116-2 between the transmitter 100 and the receiver 110 based on the detected one or more second quadrature components of the second modulated quantum signal 119 having the second polarization. The other final secret key 116-2 may be related to information of Alice's signal that is carried by the second polarization.

[0166] In the exemplary embodiment according to FIG. 7, the receiver 110 may optionally perform, with the detection part 111 and the other detection part 111-2, a joint processing to rotate the two polarizations at Bob 110 to align them with the two polarizations at Alice 100. For example, Alice's horizontal polarization may not arrive at Bob 110 as horizontal, but may be 30° from the horizontal polarization (i.e., may be 70° from the vertical polarization). The joint processing, and therefore the achieved rotation, may be performed at the detection stage (i.e., before the post-processing procedure). Alternatively, the joint processing may be performed before the operation of the polarizing beam splitter 117 using optical means. The joint processing, depicted with a vertical, dashed line in FIG. 7, may comprise a joint digital signal processing and / or a channel compensation processing.

[0167] This exemplary embodiment according to FIG. 7 provides the same advantages as the exemplary embodiment according to FIG. 1 and FIG. 6, whilst allowing the processing of two different polarizations individually, depending on the system requirements.

[0168] FIG. 8 is a schematic view of an exemplary implementation of the CV-QKD system 1 according FIG. 7. In this example, the lossy optical component 112 may comprise, or may be, a coupler or a beam splitter, or a VOA.

[0169] The polarizing beam splitter 117 may divide the one output modulated optical signal 115 received from the lossy optical component 112 into the first modulated quantum signal 118 having, for example, a horizontal polarization (as depicted in FIG. 7) and into the second modulated quantum signal 119 having, for example, a vertical polarization (as depicted in FIG. 7)The polarizing beam splitter 117 may then provide the first modulated quantum signal 118 having the horizontal polarization to the detection part 111. Then, the receiver 110 may detect, with the detection part 111, the one or more first quadrature components of the first, horizontally polarized modulated quantum signal 118.

[0170] Further, the receiver 110 may perform, with the transmitter 100, the post-processing procedure, as explained in detail above in this disclosure, to generate the final secret key 116 between Alice 100 and Bob 110 based on the detected one or more first quadrature components of the first, horizontally polarized modulated quantum signal 118, and taking into account the amount of optical loss of the lossy optical element 112. Thus, the final secret key 116 may be related to the horizontal polarization of the quantum signal 101 modulated and transmitted by Alice 100.

[0171] Then, the receiver 110 may perform, with the transmitter 100, the post-processing procedure explained in detail above in this disclosure, to generate the other final secret key 116-2 between Alice 100 and Bob 110 based on the detected one or more second quadrature components of the second, horizontally polarized modulated quantum signal 119, and taking into account the amount of optical loss of the lossy optical element 112. Thus, the other final secret key 116-2 may be associated to the horizontal polarization of the quantum signal 101 modulated and transmitted by Alice 100.

[0172] The detection part 111 and the other detection part 111-2 may be identical to each other, as depicted in FIG. 8, or each may include different components. This is not limiting in the present disclosure.

[0173] Optionally, the receiver 110 may further perform, with the detection part 111 and the other detection part 111-2, the joint processing to rotate the two polarizations at Bob 110 to align them with the two polarizations at Alice 100, as explained above for the exemplary embodiment according to FIG. 7.

[0174] FIG. 9 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds in the CV-QKD system 1 according to FIG. 1. Hereinafter, only the differences between FIG. 9 and FIG. 1 are presented. In this exemplary embodiment, the receiver 110 further comprises other lossy optical element 112-2 and other detection part 111-2.

[0175] The lossy optical element 112 and the other lossy optical element 112-2 may be equal to each other. That is, the other lossy optical element 112-2 may operate in the same manner as the lossy optical element 112 described above in the exemplary embodiments according to FIG. 1, FIG. 4, FIG. 5, FIG. 6 and FIG. 7.

[0176] The detection part 111 and the other detection part 111-2 may be equal to each other. That is, the other detection part 111-2 may operate in the same manner as the detection part 111 described above in the exemplary embodiment according to FIG. 1, FIG. 4, FIG. 5, FIG. 6 and FIG. 7.

[0177] Further, the receiver 110 comprises a polarizing beam splitter 120 that is arranged between the transmitter 100 and both the lossy optical element 112 and the other lossy optical element 112-2.

[0178] The polarizing beam splitter 120 may be configured to receive the quantum signal 101 associated to the transmitter 100, and divide it into a first modulated quantum signal 121 having a first polarization and a second modulated quantum signal 122 having a second polarization. The first polarization and the second polarization being different from each other. For example, the first polarization may be a horizontal polarization and the second polarization may be a vertical polarization. This is not limiting in this disclosure.Then, the polarizing beam splitter 120 is configured to provide the first modulated quantum signal 121 to the lossy optical element 112, and provide the second modulated quantum signal 122 to the other lossy optical element 112-2.

[0179] Thus, in this exemplary embodiment, the lossy optical element 112 may be configured to distribute the N input modulated quantum signals 121, 113 into the M output modulated quantum signals 114, 115, wherein N > 1 and M > 1, and wherein one 121 of the N input modulated quantum signals may be associated to the transmitter 100 and the other N-l input modulated quantum signals 113 different than the one 121 associated to the transmitter 100 may be vacuum signals. Further, each of the M output modulated quantum signals 114, 115 may comprise a fraction of the one input modulated quantum signal 121 having the first polarization and that is associated to the transmitter 100.

[0180] In particular, the one input modulated quantum signal 121 may be associated to the first polarization of the quantum signal 101 modulated and transmitted by the transmitter 100.

[0181] The lossy element 112 may further provide to the detection part 111 one of its M output modulated quantum signals 115, which in turn may have the first polarization.

[0182] The other lossy optical element 112-2 may be configured to distribute its respective N input modulated quantum signals 122, 113-2 into its respective M output modulated quantum signals 114-2, 115-2, wherein N > 1 and M > 1, and wherein one 122 of the N input modulated quantum signals may be associated to the transmitter 100 and the other N-l input modulated quantum signals 113-2 different than the one 122 associated to the transmitter 100 may be vacuum signals. Further, each of the M output modulated quantum signals 114-2, 115-2 of the other lossy optical element 112-2 may comprise a fraction of the one input modulated quantum signal 122 having the second polarization that is associated to the transmitter 100. In particular, the one input modulated quantum signal 122 may be associated to the second polarization of the quantum signal 101 modulated and transmitted by the transmitter 100.

[0183] The lossy element 112-2 may be further configured to provide to the other detection part 111-2 one of its respective M output modulated quantum signals 115-2, which may be referred to as other one modulated quantum signal 115-2, and that may have the second polarization.

[0184] Then, the receiver 110 may detect, with the detection part 111, one or more quadrature components of the one modulated quantum signal 115. Further, the receiver 110 may detect, with the other detection part 111-2, one or more quadrature components of the other one modulated quantum signal 115-2.

[0185] Further, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate the final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more quadrature components of both the one modulated quantum signal 115 that may have the first polarization and the other one modulated quantum signal 115-2 that may have the second polarization and that are received respectively from the lossy optical element 112 and the other lossy optical element 112-2.

[0186] Then, the receiver 110 may perform with the transmitter 100 the post-processing procedure explained above considering the one or more quadrature components of both modulated quantum signals 115 and 115-2, and taking into account the amount of optical loss of the lossy element 112 and the amount of optical loss of the other lossy element 112-2 so that the final secret key 116 between Alice 100 and Bob 110 may be generated. Said final secret key 116, thus, may be related to information carried by the two polarizations of Alice's signal.Optionally, the receiver 110 may further perform, with the detection part 111 and the other detection part 111-2, the joint processing to rotate the two polarizations at Bob 110 to align them with the two polarizations at Alice 100, as explained above.

[0187] The exemplary embodiment according to FIG. 9 provides the same advantages as the exemplary embodiment according to FIG. 1, whilst allowing the processing of two different polarizations.

[0188] FIG. 10 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds in the CV-QKD system 1 according to FIG. 9. Hereinafter, only the differences between FIG. 9 and FIG. 10 are presented.

[0189] In the CV-QKD system 1 according to FIG. 10, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate the final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more quadrature components of the one modulated quantum signal 115 that may have the first polarization and that is received from the lossy optical element 112.

[0190] Additionally, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate other final secret key 116-2 between the transmitter 100 and the receiver 110 based on the detected one or more quadrature components of the other one modulated quantum signal 115-2, which may have the second polarization and is received from the other lossy optical element 112-2.

[0191] This exemplary embodiment according to FIG. 10 provides the same advantages as the exemplary embodiment according to FIG. 9, whilst allowing the processing of two different polarizations individually, depending on the system requirements.

[0192] FIG. 11 is a schematic view of an exemplary implementation of the CV-QKD system 1 according FIG. 10. In the example according to FIG. 11, both the lossy optical component 112 and the other lossy optical element 112-2 may comprise, or may be, a coupler or a beam splitter, or a VOA.

[0193] The polarizing beam splitter 120 may divide the modulated optical signal 101 received from Alice 100 into the first modulated quantum signal 121 having, for example, a horizontal polarization and into the second modulated quantum signal 122 having, for example, a vertical polarization, as depicted in FIG. 11.

[0194] The polarizing beam splitter 120 may then provide the first modulated quantum signal 121 having the horizontal polarization to the lossy element 112. Then, the lossy element 112 may provide one output modulated quantum signal 115, which may have a horizontal polarization, to the detection part 111. Then, the receiver 110 may detect, with the detection part 111, the one or more quadrature components of the modulated quantum signal 115, which may be horizontally polarized.

[0195] Further, the receiver 110 may perform, with the transmitter 100, the post-processing procedure, as explained in detail above in this disclosure, to generate the final secret key 116 between Alice 100 and Bob 110 based on the detected one or more quadrature components of the first, horizontally polarized modulated quantum signal 115, and taking into account the amount of optical loss of the lossy optical element 112.

[0196] The polarizing beam splitter 120 may then provide the second modulated quantum signal 122 having the vertical polarization to the other lossy element 112-2. The other lossy element 112-2 may provide the other one output modulated quantum signal 115-2, which may have the vertical polarization, to the other detection part 111-2.Then, the receiver 110 may detect, with the other detection part 111-2, the one or more quadrature components of the other one modulated quantum signal 115-2, which may be vertically polarized. The receiver 110 may then perform, with the transmitter 100, the post-processing procedure explained in detail above in this disclosure, to generate the other final secret key 116-2 between Alice 100 and Bob 110 based on the detected one or more quadrature components of the other one, vertically polarized, modulated quantum signal 115-2, and taking into account the amount of optical loss of the second lossy optical element 112-2.

[0197] Optionally, the receiver 110 may further perform, with the detection part 111 and the other detection part 111-2, the joint processing to rotate the two polarizations at Bob 110 to align them with the two polarizations at Alice 100, as explained above.

[0198] FIG. 12 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds in the CV-QKD system 1 according to FIG. 1. Hereinafter, only the differences between FIG. 12 and FIG. 1 are presented. In this exemplary embodiment, the receiver 110 may further comprise other detection part 111-2, and the lossy optical element 112 may comprise, or may be, a polarizing beam splitter. That is, the lossy optical element 112 may comprise, or may be, a trusted lossy polarizing beam splitter.

[0199] The lossy polarizing beam splitter 112 may be configured to distribute the N input modulated quantum signals 113, 101 into the M output modulated quantum signals 114, 115-1, 115-2, wherein a first of the M output modulated quantum signals 115-1 has a first polarization and a second of the M output modulated quantum signals 115-2 has a second polarization. The first polarization and the second polarization are different from each other. For example and without limitation, the first and second polarizations may be, respectively, a vertical and a horizontal polarization.

[0200] Then, the lossy polarizing beam splitter 112 (i.e., the lossy optical element 112) may be configured to provide one of the output M modulated quantum signals to each of the detection parts, i.e., the detection part 111, and the other detection part 111-2.

[0201] That is, the lossy polarizing beam splitter 112 (i.e., the lossy optical element 112) may be configured to provide the first modulated quantum signal 115-1 having the first polarization to the detection part 111, and provide the second modulated quantum signal 115-2 having the second polarization to the other detection part 111-2.

[0202] Then, the receiver 110 may detect, with the detection part 111, one or more first quadrature components of the first modulated quantum signal 115-1 having the first polarization. Further, the receiver 110 may detect, with the other detection part 111-2, one or more second quadrature components of the second modulated quantum signal 115-2 that has the second polarization.

[0203] Further, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate the final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more first quadrature components of the first modulated quantum signal 115-1 having the first polarization.

[0204] Additionally, the receiver 110 may perform the post-processing procedure with the transmitter 100 to generate other final secret key 116-2 between the transmitter 100 and the receiver 110 based on the detected one or more second quadrature components of the second modulated quantum signal 115-2 having the second polarization.

[0205] Optionally, the receiver 110 may further perform, with the detection part 111 and the other detection part 111-2, the joint processing to rotate the two polarizations at Bob 110 to align them with the two polarizations at Alice 100, as explained above.

[0206] This exemplary embodiment, thus, provides the same advantages as the exemplary embodiment according to FIG. 1, whilst allowing the processing of two different polarizations individually, depending on the system requirements.Alternatively, the receiver 110 may perform the post-processing procedure with the transmitter 100 between the transmitter 100 and the receiver 110 based on both the detected one or more first quadrature components and the detected one or more second quadrature components of the first modulated quantum signal 115-1 that has the first polarization and the second modulated quantum signal 115-2 that has the second polarization, so that only one final secret key 116 between Alice and Bob is generated (not shown).

[0207] FIG. 13 is a schematic view of an exemplary implementation of the CV-QKD system 1 according FIG. 12. In the example according to FIG. 12, the first modulated quantum signal 115-1 provided by the lossy optical element 112 to the detection part 111 may have, for example, a horizontal polarization, and the second modulated quantum signal 115-2 provided by the lossy optical element 112 to the other detection part 111-2 may have, for example, a vertical polarization.

[0208] The lossy polarizing beam splitter 120 may then provide the first modulated quantum signal 115-1 having the horizontal polarization to the detection part 111, and may provide the second modulated quantum signal 115-2 having the vertical polarization to the other detection part 111-2.

[0209] Then, the receiver 110 may detect, with the detection part 111, the one or more first quadrature components of the first, horizontally polarized, modulated quantum signal 115-1. Further, the receiver 110 may detect, with the other detection part 111-2, the one or more second quadrature components of the second, vertically polarized, modulated quantum signal 115-2. The receiver 110 may further perform, with the transmitter 100, the post-processing procedure to generate the final secret key 116 between Alice 100 and Bob 110 based on the detected one or more first quadrature components of the first, horizontally polarized, modulated quantum signal 115-1, and taking into account the amount of optical loss of the lossy optical element 112.

[0210] Further, the receiver 110 may perform, with the transmitter 100, the post-processing procedure to generate the other final secret key 116-2 between Alice 100 and Bob 110 based on the detected one or more second quadrature components of the second, vertically polarized, modulated quantum signal 115-2, and taking into account the amount of optical loss of the lossy optical element 112.

[0211] Optionally, the receiver 110 may further perform, with the detection part 111 and the other detection part 111-2, the joint processing to rotate the two polarizations at Bob 110 to align them with the two polarizations at Alice 100, as explained above.

[0212] FIG. 14 is a schematic view of an exemplary embodiment of a CV-QKD system 1 according to this disclosure, which builds in the CV-QKD system 1 according to FIG. 1. Hereinafter, only the differences between FIG. 14 and FIG. 1 are presented. The CV-QKD system 1 according to FIG. 14 further comprises a calibrator 130 in communication with the receiver 110. Further, the calibrator 130 is in communication with the lossy optical element 112. The calibrator 130 is configured to perform a calibration process for the lossy optical element 112 to determine its amount of optical loss.

[0213] The calibration process is performed before the transmitter 100 modulates the quantum signal, i.e. before a QKD phase starts, and comprises the following: The calibrator 130 is configured to provide, to the lossy optical element 112, input light having an input power, and subsequently detect an output power provided by the lossy optical element 112. Then, the calibrator 130 is configured to determine the value of the optical loss of the lossy optical element 112 based on a ratio of the output power to the input power. The calibrator 130 is further configured to provide, to the receiver 110, the determined value of the optical loss of the lossy optical element 112. The calibrator 130 may be, for example and without limitation, a processor or a controller or a device capable of calibrate the lossy optical element 112.The determination, with the calibrator 130, of the value of the optical loss of the lossy optical element 112 based on a ratio of the output power to the input power comprises the following: The calibrator 130 may first calculate or the ratio of the output power to the input power. The ratio of the output power to the input power is the transmittance. In a linear scale, the transmittance is equal to 1 -(amount of optical loss). Then, the calibrator 130 may compute or calculate the amount of optical loss as being equal to one minus the value of the calculated transmittance.

[0214] Further, if the value of a total transmittance of the output power that is determined by Bob 110 is r / , a trusted transmittance before the detection of the one or more quadrature components of the one modulated quantum signal 115 is r / T. Then, a fraction of the modulated quantum signal 101 that may have been lost to Eve (that is, an amount of untrusted loss) may be determined as 1 In other words, r / Tis a trusted transmittance before the detection part 111. Then, the calibration 130 may also provide to the receiver 110 an amount of untrusted loss.

[0215] In other words, the calibration process according to this disclosure allows to determine the amount of optical loss of the lossy optical element 112 (or trusted loss) and / or the amount of untrusted loss if a part of the modulated quantum signal 101 was lost to Eve.

[0216] The amount of optical loss identified in the calibration phase may then be used in the QKD phase that has been explained above in this disclosure. That is, the "amount of optical loss" used in the post-processing procedure according to this disclosure and explained in the exemplary embodiments and exemplary implementations explained above according to FIGS. 1 to 13, refers to the amount obtained with the calibration procedure according to the embodiment of FIG. 13.

[0217] The calibration procedure may be performed as part of the QKD overall operation. The CV-QKD system 1 may cycle between a calibration phase and a QKD phase. During the calibration phase, the above calibration procedure may be performed using no QKD data. The amount of optical loss determined in the calibration phase is then used in the QKD phase that comes afterward. This is schematically depicted in FIG. 15a).

[0218] Accordingly, the CV-QKD system 1 according to this disclosure may use (in each QKD) a latest (or updated) calibrated value for the amount of optical loss of the lossy optical element 112.

[0219] Alternatively, the amount of optical loss of the lossy optical element 112 may be identified during the manufacturing phase of the CV-QKD system 1. In this case, the calibration procedure is performed only once, before the QKD starts and, accordingly, the amount of optical loss of the lossy optical element 112 is calibrated once for the lifetime of the CV-QKD system 1, as schematically depicted in FIG. 15b).

[0220] In this case, the QKD phase uses a value that may be outdated over time. Notably, even when the amount of optical loss is calibrated only once, the advantages of the CV-QKD system 1 according to this discloser are achieved, i.e., the reach of the final secret key 116 obtained with the post-processing procedure according to this disclosure is enhanced.

[0221] In this exemplary embodiment, QKD data means the data that participates in the QKD protocol and is the initial form of the final secret key 116. Specifically, it is related to the choices of the quantum states sent by Alice 100 or the measurement outcomes obtained by Bob 110 measuring (or detecting), with the detection part 111, the quantum states received through the quantum channel 102 via the lossy optical element 112.FIG. 17 shows an exemplary embodiment of a method 1700 for a CV-QKD system 1. The CV-QKD system 1 comprises a transmitter 100 and a receiver 110, the receiver 110 comprising a detection part 111 and a lossy optical element 112, and the lossy optical element 112 is arranged between the transmitter 100 and the detection part 111.

[0222] The method 1700 may be carried out by the CV-QKD system 1 according to this disclosure and explained above in the exemplary embodiments according to any one of FIG. 1, FIG. 4, FIG. 5, FIG. 6, FIG. 7, FIG. 9. FIG. 10, FIG. 12 and FIG. 13. The method 1700 comprises a step 1701 of modulating, with the transmitter 100, a quantum signal according to a discrete or continuous distribution in phase and amplitude. Then, the method 1700 comprises a step 1702 of sending to the receiver 110, with the transmitter 100, the modulated quantum signal 101 through a quantum channel 102.

[0223] The method 1700 further comprises a step 1703 of distributing, with the lossy optical element 112, N input modulated quantum signals 101, 113 into M output modulated quantum signals 114, 115, where N > 1 and M > 1. One 101 of the N input modulated quantum signals is associated to the transmitter 100 and the other N-l input modulated quantum signals 113 different than the one 101 associated to the transmitter 100 are vacuum signals, and each of the M output modulated quantum signals 114, 115 comprises a fraction of the one input modulated quantum signal associated to the transmitter 100.

[0224] Further, the method 1700 comprises a step 1704 of providing to the detection part 111, with the lossy optical element 112, one 115 of the M output modulated quantum signals. The lossy optical element 112 is arranged in a location in the receiver 110 that is inaccessible to an eavesdropper.

[0225] The method 1700 further comprises a step 1705 of detecting, with the detection part 111 of the receiver 110, one or more quadrature components of the one modulated quantum signal 115 received from the lossy optical element 112.

[0226] Further, in a step 1706, the method 1700 comprises performing, with the receiver 110, a post-processing procedure with the transmitter 100 to generate a final secret key 116 between the transmitter 100 and the receiver 110 based on the detected one or more quadrature components of the one modulated quantum signal 115 and an amount of optical loss of the lossy optical element 112.

[0227] The method 1700 may further comprise actions according to the described aforementioned embodiments of the CV-QKD system 1. Hence, the method 1700 achieves the same advantages as the CV-QKD system 1.

[0228] The present disclosure further provides a computer program comprising instructions that, when the program is executed by a computer, cause the computer to carry out the steps of the method 1700 performed the lossy optical element 112.

[0229] Additionally or alternatively, the computer program comprises instructions that, when the program is executed by a computer, cause the computer to carry out the steps of the method 1700 performed by the detection part 111.

[0230] Additionally or alternatively, the computer program comprises instructions that, when the program is executed by a computer, cause the computer to carry out the steps of the method 1700 performed by the receiver 110 and / or by the transmitter 100.

[0231] The computer program may be included in a computer readable medium. The computer readable medium may comprise essentially any memory, such as a ROM (Read-Only Memory), a PROM (Programmable Read-Only Memory), a 15 EPROM (Erasable PROM), a Flash memory, an EEPROM (Electrically Erasable PROM), or a hard disk drive.

[0232] The computer program achieves the same advantages as the method 1700 and as the CV-QKD system 1.The present disclosure has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed matter, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the disclosure the word "comprising" does not exclude other elements or steps and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

CLAIMS1. A continuous Variable-Quantum Key Distribution, CV-QKD, system (1) comprising a transmitter (100) and a receiver (110), the receiver (110) comprising a detection part (111) and a lossy optical element (112), the lossy optical element (112) being arranged between the transmitter (100) and the detection part (111), wherein:the transmitter (100) is configured to:modulate a quantum signal (101) according to a discrete or continuous distribution in phase and amplitude; and send to the receiver (110) the modulated quantum signal (101) through a quantum channel (102); the lossy optical element (112) is configured to:distribute N input modulated quantum signals (101, 113) into M output modulated quantum signals (114, 115), wherein N > 1 and M > 1, wherein one (101) of the N input modulated quantum signals is associated to the transmitter (100) and the other N-l input modulated quantum signals (113) different than the one (101) associated to the transmitter (100) are vacuum signals, and wherein each of the M output modulated quantum signals (114, 115) comprises a fraction of the one (101) input modulated quantum signal associated to the transmitter (100);provide, to the detection part (111), one ( 115 ) of the M output modulated quantum signals;wherein the lossy optical element (112) is arranged in a location in the receiver (110) that is inaccessible to an eavesdropper; andthe receiver (110) is configured to:detect, with the detection part (111), one or more quadrature components of the one modulated quantum signal (115) received from the lossy optical element (112); andperform a post-processing procedure with the transmitter (100) to generate a final secret key (116) between the transmitter (100) and the receiver (110) based on the detected one or more quadrature components of the one (115) modulated quantum signal and an amount of optical loss of the lossy optical element (112).

2. The CV-QKD system (1) according to claim 1, wherein the lossy optical element (112) is configured to maintain inaccessible to the eavesdropper the other (114) of the M modulated quantum signals different than the one (115) modulated quantum signal provided to the detection part (111).

3. The CV-QKD system (1) according to claims 1 or 2, wherein the lossy optical element (112) comprises a plurality of N x M ports (1121, 1122), each of the N ports (1121) being an input port and each of the M ports (1122) being an output port.

4. The CV-QKD system (1) according to one of the claims 1 to 3, wherein the lossy optical element (112) comprises a beam splitter, a polarizing beam splitter, an optical coupler, or a variable optical attenuator.

5. The CV-QKD system (1) according to one of the claims 1 to 4, wherein the receiver (110) further comprises a polarizing beam splitter (117), the polarizing beam splitter (117) being arranged between the lossy optical element (112) and the detection part (111); andwherein the polarizing beam splitter (117) is configured to:divide the one modulated quantum signal (115) associated to the transmitter (100) received from the lossy optical element (112) into a first modulated quantum signal (118) having a first polarization and a second modulated quantum signal (119) having a second polarization, the first polarization and the second polarization being different from each other; andprovide each of the first modulated quantum signal and the second modulated quantum signal to the detection part (111).

6. The CV-QKD system (1) according to one of the claims 1 to 4, wherein the receiver (110) further comprises a polarizing beam splitter (120), other lossy optical element (112-2) and other detection part (111-2), the polarizing beam splitter (120) being arranged between the transmitter (100) and both the lossy optical element (112) and the other lossy optical element (112-2); andwherein the polarizing beam splitter (120) is configured to:divide the modulated quantum signal (101) associated to the transmitter (100) into a first modulated quantum signal (121) having a first polarization and a second modulated quantum signal (122) having a second polarization, the first polarization and the second polarization being different from each other; and provide the first modulated quantum signal (121) to the lossy optical element (112) and provide the second modulated quantum signal (122) to the other lossy optical element (112-2).

7. The CV-QKD system (1) according to one of the claims 1 to 4, wherein when the lossy optical element (112) comprises the polarizing beam splitter and the receiver (110) comprises other detection part (111-2), the lossy optical element (112) is configured to:distribute the N input modulated quantum signals (113, 101) into the M output modulated quantum signals (114, 115), wherein a first of the M modulated quantum signals (115-1) has a first polarization and a second of the M modulated quantum sub-signals (115-2) has a second polarization, the first polarization and the second polarization being different from each other; andprovide the first modulated quantum signal (115-1) to the detection part (111) and provide the second modulated quantum signal (115-2) to the other detection part (111-2).

8. The CV-QKD system (1) according to one of the claims 1 to 7, wherein the post-processing procedure to generate the final secret key between the transmitter (100) and the receiver (110) comprises: a parameter estimation step that takes into account the amount of optical loss of the lossy optical element (112), and a privacy amplification step that takes into account the amount of optical loss of the lossy optical element (112).

9. The CV-QKD system (1) according to claim 8, wherein the parameter estimation step that takes into account the amount of optical loss of the lossy optical element (112), comprises:the receiver (110) is configured to determine, with the transmitter (100), an amount of noise and an amount of loss introduced by the quantum channel to the modulated quantum signal sent by the transmitter (100) before it reaches the receiver (110) by using the amount of optical loss of the lossy optical element (112), wherein an optical loss of the lossy optical element (112) is inaccessible to the eavesdropper.

10. The CV-QKD system (1) according to one of the claims 8 or 9, wherein the privacy amplification step that takes into account the amount of optical loss of the lossy optical element (112), comprises:the receiver (110) is configured to perform, with the transmitter (100), hashing on an error corrected key to obtain the final secret key (116) using a compression ratio calculated by taking into account the amount of the optical loss of the lossy optical element (112) and by taking into account the other of the M output modulated quantum signals different than the one modulated quantum signal provided to the detection part (111) and that are inaccessible to the eavesdropper.

11. The CV-QKD system (1) according to one of the claims 8 to 10, wherein the post-processing procedure further comprises one or more of: a sifting step, a symbol mapping step, and an information reconciliation step.

12. The CV-QKD system (1) according to one of the preceding claims, further comprising a calibrator (130); wherein, before the transmitter (100) modulates the quantum signal, the calibrator (130) is configured to perform a calibration process for the lossy optical element (112) to determine its amount of optical loss.

13. The CV-QKD system (1) according to claim 12, wherein the calibration process for the lossy optical element (112) to determine its amount of optical loss comprises:the calibrator (130) is configured to:provide, to the lossy optical element (112), input light having an input power, and detect an output power provided by the lossy optical element (112);determine the value of the optical loss based on a ratio of the output power to the input power; and provide, to the receiver (110), the determined value of the optical loss of the lossy optical element (112).

14. A method (1700) for a continuous Variable-Quantum Key Distribution, CV-QKD, system (1), the system comprising a transmitter (100) and a receiver (110), the receiver (110) comprising a detection part (111) and a lossy optical element (112), the lossy optical element (112) being arranged between the transmitter (100) and the detection part (111), and wherein the method (1700) comprises:modulating (1701), with the transmitter (100), a quantum signal according to a discrete or continuous distribution in phase and amplitude;sending (1702) to the receiver (110), with the transmitter (100), the modulated quantum signal through a quantum channel;distributing (1703), with the lossy optical element (112), N input modulated quantum signals into M output modulated quantum signals, wherein N > 1 and M > 1, wherein one of the N input modulated quantum signals is associated to the transmitter (100) and the other N-l input modulated quantum signals different than the one associated to the transmitter (100) are vacuum signals, and wherein each of the M output modulated quantum signals comprises a fraction of the one input modulated quantum signal associated to the transmitter (100);providing (1704) to the detection part (111), with the lossy optical element (112), one of the M output modulated quantum signals; wherein the lossy optical element (112) is arranged in a location in the receiver (110) that is inaccessible to an eavesdropper;detecting (1705), with the detection part (111) of the receiver (110), one or more quadrature components of the one modulated quantum signal received from the lossy optical element (112); andperforming (1706), with the receiver (110), a post-processing procedure with the transmitter (100) to generate a final secret key between the transmitter (100) and the receiver (110) based on the detected one or more quadrature components of the one modulated quantum signal and an amount of optical loss of the lossy optical element (112).

15. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method steps performed by the receiver (110) and / or by the lossy optical element (112) of the receiver (110) and / or by the detection part (111) of the receiver (110), according to claim 14.

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