Ml based security proof of quantum communication protocols with noisy quantum channels

Abstract

Disclosed is a method for sharing information using a data sharing system comprising a sender node and a receiver node using a noisy quantum channel in accordance with a quantum communication protocol, the method comprising: providing a trained machine learning model, the machine learning model being configured to receive a set of parameters of a given system and noise model in order to predict whether the given system is secure or unsecure for sharing information according to the quantum communication protocol, the set of parameters indicating a level of success of an attack by a third party and a reception success at a receiver node of the given system and being descriptive of the given system; evaluating the set of parameters for the data sharing system for sharing the information; inputting the evaluated set of parameters and the noise model to the machine learning model, thereby receiving a prediction of a security of the data sharing system; aborting the quantum communication protocol if the data sharing system is predicted as being unsecure.

Description

ML BASED SECURITY PROOF OF QUANTUM COMMUNICATION PROTOCOLS WITH NOISY QUANTUM CHANNELSFIELD OF THE INVENTION

[0001] The invention relates to the field of data communication, and particularly to a method for sharing information between nodes using a noisy quantum channel in accordance with a quantum communication protocol.BACKGROUND

[0002] Quantum communication is a field that uses the quantum mechanical properties of a quantum system; properties like superposition and entanglement, to enable secure and efficient communication protocols. It offers a wide range applications like Quantum Key Distribution (QKD) which enables two parties to securely exchange cryptographic keys between them, wherein any attempt to intercept the quantum signal by a third party may disturb the quantum state, alerting the legitimate users. Another major application of quantum communication is the quantum teleportation and quantum cryptography. However, there is a need for improved use of QKD.SUMMARY

[0003] It is an objective to provide a method for sharing information using a data sharing system comprising a sender node and a receiver node using a noisy quantum channel in accordance with a quantum communication protocol. The objectives underlying the invention are solved by the features of the independent claims.

[0004] Embodiments provide a method for sharing information using a data sharing system comprising a sender node and a receiver node using a noisy quantum channel in accordance with a quantum communication protocol, the method comprising: providing a trained machine learning model, the machine learning model being configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system in order to predict whether the given system is secure or unsecure for sharing information according to the quantum communication protocol, the set of parameters indicating a level of success of an attack by a third party and a level of reception success at a receiver node of the given system and being descriptive of the given system; determining a noise model for a noise of the noisy quantum channel of the data sharing system; evaluating the set of parameters for the data sharing system for sharing the information; inputting the evaluated set of parameters and the noise model to the machine learning model, thereby receiving a prediction of a security of the data sharing system; aborting the quantum communication protocol if the data sharing system is predicted as being unsecure.

[0005] Embodiments provide a computer program comprising instructions for causing a computer system for performing the method of the above embodiment.

[0006] Embodiments provide a computer system for controlling a data sharing system comprising a sender node and a receiver node, the data sharing system being configured for information sharing using a noisy quantum channel in accordance with a quantum communication protocol, the computer system being configured for: providing a trained machine learning model, the machine learning model being configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system in order to predict whether the given system is secure or unsecure for sharing information according to the quantum communication protocol, the set of parameters indicating a level of success of an attack by a third party and a level of reception success at a receiver node of the given system and being descriptive of the given system; determining a noise model for a noise of the noisy quantum channel of the data sharing system; evaluating the set of parameters for the data sharing system forsharing the information; inputting the evaluated set of parameters and the noise model to the machine learning model, thereby receiving a prediction of a security of the data sharing system; causing an abortion of the quantum communication protocol if the data sharing system is predicted as being unsecure.

[0007] It is understood that one or more of the aforementioned embodiments may be combined as long as the combined embodiments are not mutually exclusive.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In the following, examples are described in greater detail making reference to the drawings in which:

[0009] Fig. 1 is a block diagram of a system in accordance with an example of the present subject matter.

[0010] Fig. 2 is a diagram illustrating a machine learning model in accordance with an example of the present subject matter.

[0011] Fig. 3 is a flowchart of a method for sharing information between a sender node and a receiver node in accordance with a quantum communication protocol.

[0012] Fig. 4 is a flowchart of a security proof method in accordance with the quantum communication protocol.

[0013] Fig. 5A is a diagram representing an example quantum communication system in accordance with an example of the present subject matter.

[0014] Fig. 5B schematically depicts an example quantum circuit system for the third-party quantum computing system in accordance with an example of the present subject matter.

[0015] Fig. 5C schematically depicts an example quantum circuit system for the third-party quantum computing system in accordance with an example of the present subject matter.

[0016] Fig. 5D schematically depicts an example quantum circuit system for the third-party quantum computing system in accordance with an example of the present subject matter.

[0017] Fig. 6A is a diagram representing an example quantum communication system in accordance with an example of the present subject matter.

[0018] Fig. 6B schematically depicts an example quantum circuit system for the third-party quantum computing system in accordance with an example of the present subject matter.

[0019] Fig. 7 is a flowchart of a method for optimizing the parameters of a quantum circuit system in accordance with an example of the present subject matter.DETAILED DESCRIPTION

[0020] In the following, similar elements are denoted by the same reference numerals.

[0021] The present subject matter may enable two or more distant parties to communicate securely with each other. In particular, the present subject matter may provide an accurate evaluation of the security level of the communication through the noisy quantum channels.

[0022] Quantum computing may enable secure access to information. For that, quantum channels may be used. The quantum channel may be a communication channel which may transmit quantum information. The quantum channel may further be used to transmit classical information. An example of quantum information may be information that indicates the state of a qubit. The state of the qubit may refer to the computational basis state of a given basis. The qubit may physically be implemented using a quantum system having two states, wherein the quantum system may, for example, be a photon or ion. The quantum channel may, for example, be implemented using optical fibers or free space. For example, the vertical and horizontal photon’s polarization may be used as a qubit state. The two energy levels of an ion may, for example, be used as a qubit state. For example, incase of a qubit represented by a photon, the computational basis states may be horizontal and vertical polarization states or may be diagonal and antidiagonal polarization states.

[0023] The quantum channel may be used to share or provide information. For example, a system (named data sharing system or quantum communication system) comprising sender and receiver nodes is provided. The sender node may, for example, comprise a sender quantum computing system and the receiver node may, for example, comprise a receiver quantum computing system. The terms "receiver node" and "receiver quantum computing system" are used interchangeably. The terms "sender node" and "sender quantum computing system" are used interchangeably. The data sharing system may comprise the sender quantum computing system which is connected through the quantum channel with the receiver quantum computing system. The quantum channel quantum channel may be subject to one or more types of noise. The quantum channel may thus be referred to as noisy quantum channel. The noise of the noisy quantum channel may refer to the noise to which the noisy quantum channel is exposed. The noise may introduce errors, decoherence, and other forms of degradation to the transmitted quantum information. For example, the amplitude damping noise may arise from interactions with the surrounding noisy environment, such as thermal fluctuations or other sources of energy dissipation. The amplitude damping noise may affect the amplitude of a quantum state, causing it to decay over time, leading to errors in the transmitted information. In another example, the phase damping noise may arise from interactions with the surrounding environment, such as fluctuations in the phase of the quantum system or other sources of phase decoherence. The phase damping noise may be a form of decoherence that affects the phase of a quantum state, causing it to decay over time, leading to errors in the transmitted information. The data sharing system may be described by system parameters such as a distance between the sender and receiver nodes, a detector efficiency of a signal detector at the receiver node and design parameters of components of the data sharing system. The system parameters may further indicate the amount of information that is shared between the sender node and the receiver node. In one example, the system parametersmay further comprise Quantum Bit-Error Ratio (QBER). The data sharing system may be a real system (i.e., not simulated system) which is being used for real sharing of information through the noisy quantum channel.

[0024] For example, the sender quantum computing system may use the noisy quantum channel to share information with the receiver quantum computing system or vice versa. The shared information may, for example, be encoded in states of qubits that travel through the noisy quantum channel from the sender quantum computing system to the receiver quantum computing system.

[0025] The sharing of the information between the sender quantum computing system and the receiver quantum computing system may be performed in accordance with the quantum communication protocol. The quantum communication protocol may be a system of rules that allows two or more entities of a communications system to share (e.g., transmit) information. The quantum communication protocol may, for example, define the rules, syntax, semantics, and synchronization of communication and possible error recovery methods. In one example, the quantum communication protocol may be used by the sender quantum computing system and the receiver quantum computing system for obtaining two identical copies of a sequence of bits, wherein the shared information may comprise at least the sequence of bits. The sequence of bits may, for example, be random and secret. The sender quantum computing system may, for example, prepare qubits in states representing the sequence of bits respectively. The quantum communication protocol may, for example, be a single-qubit-based protocol or entangled-state-based protocol.

[0026] The present subject matter may enable two or more distant parties to communicate securely with each other. In particular, the present subject matter may provide an accurate evaluation of the security level of the communication through the noisy quantum channel taking into account errors which may be introduced by both the noise of the noisy quantum channel and the eavesdropping. For that, a third-party quantum computing system (also referred to as the third party) may be provided. The third-party quantum computing system may be configured to connectto the noisy quantum channel between the sender quantum computing system and the receiver quantum computing system. The sender quantum computing system may prepare qubits in respective basis states and send them through the noisy quantum channel to the receiver quantum computing system. The receiver quantum computing system may be configured to receive the prepared qubits through the noisy quantum channel, and measure their states. The third-party quantum computing system may be configured to intercept the prepared qubits on the noisy quantum channel and determine or estimate their states and send the intercepted qubits to the receiver node through the noisy quantum channel. In one example, the third-party quantum computing system may be configured to intercept the prepared qubits on the noisy quantum channel and determine their states without destroying or changing the states of the intercepted qubits and send the qubits to the receiver node through the noisy quantum channel. In one example, the third-party quantum computing system may be configured to intercept the prepared qubits on the quantum channel, create approximate copies of the intercepted qubits send the approximate copies to the receiver node through the noisy quantum channel and use the approximate copy of the intercepted qubit to estimate the state of the intercepted qubit. The third-party quantum computing system may enable to simulate attacks or eavesdropping on the noisy quantum channel. The third-party quantum computing system may be used to evaluate the level of success of an attack (i.e. , the level of success of eavesdropping the noisy quantum channel). For example, the third-party quantum computing system may be used to evaluate a first metric that represents the level of success of an attack. The first metric may, for example, be a distance measure such as a fidelity. For example, the third-party quantum computing system may be used to determine elements of the density matrices that may be used to compute the fidelity between the state of the intercepted qubit and a state of the prepared qubit as prepared by the sender node. Each quantum computing system of the sender quantum computing system, the receiver quantum computing system and the third-party quantum computing system may, for example, comprise a quantum circuit system. The quantum circuit system may utilize the principles of quantum mechanics to perform quantum computations by operating one or more qubits. Said quantum circuit system may further utilize the principles of quantum mechanics to performquantum communication to transmit or receive quantum information. The quantum circuit system may, for example, be a quantum computer. For example, the each quantum computing system may be a photonic quantum computer using photons to represent the qubits, wherein the quantum circuit system may, for example, comprise components such as: a polarization controller, a pulse pattern generator, a light source, a planar light-wave circuit or any other component that may enable the quantum circuit system to perform quantum computation and / or quantum communication. The each quantum computing system may, for example, be configured to perform classical computations using a classical computer or by simulating classical computations. The classical computer may or may not be part of the each quantum computing system. The classical computer may include the hardware such as processor and memory and software such as an operating system. The receiver quantum computing system may be used to evaluate the level of reception success. For example, the receiver quantum computing system may be used to evaluate a second metric that represents the level of reception success. The second metric may, for example, be a distance measure such as a fidelity. For example, the receiver quantum computing system may be used to determine elements of the density matrices that may be used to compute the fidelity between the state of the received qubit and a state of the prepared qubit as prepared by the sender node.

[0027] The third-party quantum computing system may be configured to provide a third-party quantum system. The third-party quantum computing system may be defined according to an attack configuration of a simulated attack. For example, the third-party quantum system may be defined by the prepared qubit which is intercepted on the noisy quantum channel and a set of one or more additional qubits. For example, the third-party quantum computing system may comprise the quantum circuit system which comprises the intercepted qubit and the set of additional qubits. The quantum circuit system may further be configured to perform a set of one or more quantum operations having specific parameters. The quantum operation may be a unitary operation. The application of the set of one or more quantum operations may enable to determine or predict the state of the intercepted qubit (without destroying its state) by measuring one or more additional qubits ofthe quantum circuit system after application of the set of one or more quantum operations. After application of the set of one or more quantum operations, the intercepted qubit may remain unchanged and may be resent by the quantum circuit system to the receiver node through the noisy quantum channel. The quantum operation may, for example, be one operation or a sequence of operations of a defined set of universal quantum gates including, for example, the rotation operators and controlled NOT (CNOT) operator.

[0028] For example, the set of one or more quantum operations may be a controlled operation using the intercepted qubit as a control qubit. The controlled operation may, for example, be a controlled rotation applied on the additional qubit and using the intercepted qubit as control qubit. The controlled operation may, for example, be CNOT operation that acts on two qubits in order to perform the NOT operation on the additional qubit based on the state of the intercepted qubit. After application of the controlled operation, the intercepted qubit may remain unchanged and may be resent by the quantum circuit system to the receiver node through the noisy quantum channel. After application of the controlled operation, the state of the additional qubit involved in the controlled operation may indicate the state of the intercepted qubit. In another example, the set of quantum operations may comprise the controlled operation in addition to additional quantum operations. The additional quantum operations may be applied on at least part of the set of additional qubits. After application of the set of quantum operations, at least one of the set of additional qubits may be measured and the result of the measurement may be used to determine or estimate the state of the intercepted qubit.

[0029] For example, the third-party quantum computing system may comprise control means that control the states of the qubits of the quantum circuit system e.g., that control the quantum circuit system to perform the set of quantum operations. The quantum operation may be applied on at least part of the qubits of the quantum circuit system. The quantum operation may be a controlled quantum operation, where the intercepted qubit acts as a control for the quantum operation. The specific parameters of the quantum circuit system may, for example, be parameters of the quantum operations such as rotation angles of rotationoperations. For example, the state of the qubit may be transformed by rotating it around axis x, y, and z in the Bloch sphere.

[0030] However, the noise affecting the qubits may lead to decoherence, and the qubits obtained at the receiver node may not be exactly what were expected in the absence of noise. Thus, one may have to deal with the disturbance induced due to eavesdropping and the noise of the noisy quantum channel. For that, the machine learning (ML) model may be used. The noise of the noisy quantum channel of the data sharing system may be described by a noise model. The noise model indicates at least one of: depolarizing channel noise, amplitude damping channel noise, phase damping channel noise or bit flip channel noise. For example, the type of noise of the noisy quantum channel of the data sharing system may be determined by a user of the data sharing system. Alternatively, the type of noise of the noisy quantum channel of the data sharing system may be determined by using, for example, metadata descriptive of the data sharing system.

[0031] For example, in order to predict the security of sharing information using the data sharing system (e.g., being used in real time), the machine learning model may be used. This refers to the inference phase of the machine learning model. The machine learning model may be defined as follows. The machine learning model is configured to receive as input the values of the set of parameters which are evaluated for a given system, wherein the given system comprises a given receiver node and a given sender node which are configured to share information through a given noisy quantum channel connecting the given receiver node to the given sender node in accordance with the quantum communication protocol and a noise model of a noise of the given noisy quantum channel. In addition, the machine learning model may receive as input the noise model that is descriptive of the noise of the given noisy quantum channel of the given system. The noise model may, for example, be encoded using techniques such as one-hot encoding to convert it into a numerical format that machine learning algorithms can understand. In response to receiving the values of the set of parameters and the noise model, the machine learning model may provide an output, wherein the output indicates whether the given system is secure or unsecure for sharing information. For example, themachine learning model may be trained with different noise models such that the input noise model may be used by the trained machine learning model to predict the security of the data sharing system making use of what has been learnt for that noise model.

[0032] The set of parameters which are input to the trained machine learning model (e.g., in the inference phase) comprise the system parameters and the values of the first and second metrics of the data sharing system. For example, in addition to the system parameters of the data sharing system, the values of the first metric and the second metric and the noise model may be provided as input to the trained machine learning model. In response to receiving the input (i.e. , values of the set of parameters and the noise model), the trained machine learning model may predict whether the data sharing system is secure or unsecure. The data sharing system is secure means that the sharing of the information (e.g., the sequence of bits) is secure and thus the sharing is not aborted. The data sharing system is unsecure means that the sharing of the information (e.g., the sequence of bits) is unsecure and thus the sharing is aborted so that the shared information may not be used as the third party may have access to it. Thus, the trained machine learning model may automatically detect abnormal combination of the set of parameters and classify them into a secure or unsecure system. This may provide a universal attack detection or prevention model, which can recognize or prevent attacks by, for example, using a forward propagation calculating process.

[0033] In one example, the system parameters may comprise a first subset of parameters which describe the design (e.g., structure and components) of the data sharing system and a second subset that the describe the operation of the data sharing system. The second subset of parameters may comprise at least one of: the amount of information (e.g., the number of bits) being shared by the data sharing system or the time at which the data sharing is performed by the data sharing system. The second subset of parameters may enable an adaptable description of the data sharing system based on its operation. This may enable accurate classification of the data sharing system.

[0034] Aborting the quantum communication protocol may, for example, comprise providing a warning or error signal to the sender quantum computing system and the receiver quantum computing system. The signal may indicate that the communication is not secure and that the shared information may be accessed by an eavesdropper.

[0035] In one example, upon receiving the warning signal, the sender quantum computing system and the receiver quantum computing system may share the information by adapting the quantum communication protocol or may repeat the information sharing at another point of time or may stop sharing information. In one example, in response to aborting the quantum communication protocol, the information may be shared again (e.g., at a later point of time) between the sender quantum computing system and the receiver quantum computing system, the set of parameters may be evaluated and a further check using the trained ML model whether to abort or not the quantum communication protocol may be performed. This may be advantageous in case the security issue is temporal e.g., it may only occur due to some temporal misconfigurations. In one example, in response to aborting the quantum communication protocol, the quantum communication protocol may be adapted and the method may be repeated using the adapted quantum communication protocol.

[0036] In one example, if the data sharing system is secure, the shared information may be classified as being secure and thus can be used by the sender and the receiver nodes. For example, if the system is predicted as being secure, the quantum communication protocol may not be aborted and its execution may continue in order to share the information between the sender node and the receiver node.

[0037] In one example, the first metric may be the fidelity between the state of the intercepted qubit as determined or estimated by the third-party and a state of the prepared qubit as prepared by the sender. The state of the prepared qubit may be represented by a density matrix p and the state of the intercepted qubit may be represented by a density matrix p2. The first metric may thus be defined as follows:F2This may enable to compare the effects of noise on qubits in terms of the fidelity of the qubits prepared at the sender node and the qubits obtained at the third party by considering various noisy quantum channels through which the qubits travel. For example, in case of the amplitude damping noise, the noise may be characterized by Kraus operators so that the evolution of the state of the prepared qubit may be modeled by applying the Kraus operators.

[0038] In one example, the quantum communication protocol may be used by the sender quantum computing system and the receiver quantum computing system for obtaining two identical copies of a sequence of bits, wherein the shared information may be the sequence of bits. The sequence of bits may, for example, be random and secret. The third-party quantum computing system may try to learn original bits. During this sharing of information process, each of the three parties may obtain a string of bits. The three strings may be interpreted as binary random variables. The degree of dependence between two random variables may be measured in terms of the mutual information. In one example, the first metric may alternatively comprise the mutual information (transinformation) between binary random variables of the sender node and of the third party. The first metric may be the mutual information (transinformation) between binary random variables of the sender node and of the third party. The mutual information may, for example, be defined as follows: l(X, T) = where X may be the randomvariable associated with bits at the sender quantum computing system and Y may be the random variable associated bits at the third-party quantum system, where p(x,y) is the joint probability, and p(x) and p(y) are the individual probabilities.

[0039] The second metric may be a fidelity between the state of the prepared qubit as prepared by the sender node and the measured state of the qubit which is received at and measured by the receiver quantum computing system. The state of the prepared qubit may be represented by a density matrix p and the state measured by the receiver quantum computing system may be represented by a density matrix p2. The second metric may thus be defined as follows: F1(p1, p2) = tr ] / pip2 / pi)2■ This may enable to compare the effects of noise andeavesdropping on qubits in terms of the fidelity of the qubits prepared at the sender node and the qubits obtained at the receiver node by considering various noisy quantum channels through which the qubits travel. The references Charles H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin. Experimental quantum cryptography. Journal of cryptology, 5:3-28 and llrnesh Vazirani and Thomas Videck. Fully device-independent quantum key distribution. Physical Review Letters, 113(14), Sep 2014 provide example implementations for the evaluation of the first metric and the second metric.

[0040] For example, a quantum state tomography may be used to determine the fidelities of the first and second metrics. For example, the quantum state tomography may be used to construct the density matrices p and p2e.g., with a series of measurements performed in different bases, and estimate the fidelity. The first and second metrics may be evaluated using a metric determination system. The metric determination system may or may not be part of the third-party quantum computing system. For example, the metric determination system may use quantum state tomography to construct the density matrices p and p2e.g., with a series of measurements performed in different bases, and estimate the fidelity.

[0041] In one example, the trained machine learning model may be a classical machine learning model such as a deep neural network. Alternatively, the trained machine learning model may be a quantum machine learning model such as quantum neural network (QNN).

[0042] The quantum communication protocol may, for example, be BB84 protocol or Eckert protocol E91. The data sharing system may be configured to share information between the sender node and the receiver node in accordance with the BB84 protocol. The quantum communication protocol may, for example, be a single-qubit-based protocol or entangled-state-based protocol. The single-qubit based protocol may be referred to as prepare and measure (P&M) protocol.

[0043] In one example, the information may be shared between the sender quantum computing system and the receiver quantum computing system by atleast: sending by the sender quantum computing system qubits to the receiver quantum computing system. The sender quantum computing system may prepare each qubit in a respective computational basis state before sending the prepared qubit through the noisy quantum channel to the receiver quantum computing system. The states of the prepared qubits provide the information shared between the sender quantum computing system and the receiver quantum computing system. This example may be advantageous as it may enable a seamless integration of the present subject matter with existing communication protocols e.g., the quantum communication protocol may be the BB84 protocol. For example, the sender quantum computing system may prepare the qubit using predefined bases. For example, in order to encode or prepare a qubit, the sender quantum computing system may select one of the predefined bases and prepare the qubit in a computation basis state using the selected base. The receiver quantum computing system may measure the prepared qubit once received over the noisy quantum channel by selecting a base of the predefined bases and using the selected base to measure the prepared qubit which is received at the receiver quantum computing system. This example may enable the sharing of information in accordance with the single-qubit-based protocol.

[0044] In one example, the information may be shared between the sender quantum computing system and the receiver quantum computing system by using entanglement. For that, a two-qubit system may be defined for each pair of qubits of a set of pairs of qubits, where one qubit of the two-qubit system may be part of the sender quantum computing system and the other qubit may be part of the receiver quantum computing system. The state of the two-qubit system may be an entangled state. For example, the entangled state of the two-qubit system may be any one of the Bell states e.g., the sender quantum computing system and the receiver quantum computing system may each receive one photon of a polarization- entangled pair.

[0045] The present subject matter may make use of the entangled state of the two- qubit system to transmit or share information between the sender quantum computing system and the receiver quantum computing system. The informationmay be teleported from the sender’s qubit to the receiver’s qubit by means of entanglement. For example, the two qubits may be entangled such that when a particular property is measured in one qubit, the opposite state may be observed on the entangled qubit instantaneously.

[0046] The entangled state may be provided as a distributed entangled state such that the entangled pair of qubits are located at different locations i.e. , in the sender quantum computing system and the receiver quantum computing system respectively. The distributed entangled state between the pair of qubits may, for example, be formed by first forming locally at the sender quantum computing system the entangled state of the pair of qubits, and subsequently sending by the sender quantum computing system one of the pair of qubits to the receiver quantum computing system. The entangled state may, for example, be formed by applying a CNOT operation on the pair of qubits. Thus, for sharing the information between the sender quantum computing system and the receiver quantum computing system, multiple distributed entangled states may be created using the pairs of qubits respectively. Using entanglement may further secure the sharing of information in accordance with the present subject matter. In one example, the quantum communication protocol may be an Entangled QKD protocol e.g., an entangled BB84 variant.

[0047] In one example, the sender quantum computing system and the receiver quantum computing system may further be configured to communicate through a classical public channel e.g., to exchange public data such as the bases used to prepare or measure the qubits. The third-party quantum computing system may be configured to intercept and receive data communicated on the classical public channel. The third-party quantum computing system may, for example, use this intercepted information for determining or improving the attack configuration and for determining the first metric.

[0048] The generation of the training data for training the machine learning model may make use of the security bounds used by the quantum communication protocol. The quantum communication protocol may control the security of thesharing of information taking into account the noise of the noisy quantum channel. For that, the quantum communication protocol may use the security bounds which are adapted to the noise model of the noise of the noisy quantum channel. Indeed, the security bounds may be affected by the noise. In particular, different noise types may affect differently the security bounds. The security bounds may, for example, be defined for different noise models by using a theoretical method through theoretical analysis, a simulation method by creating models and performing simulations on the modeled systems, or a statistical method by analyzing data and using statistical techniques to identify patterns. This definition of the security bounds may enable to create the training dataset dependent on the noise model.

[0049] A security bound may be defined for the reception of the qubits at the receiver node. For example, this security bound may be named or referred to as the error tolerance bound. The error tolerance bound may refer to a value or a range of values. The error tolerance bound may refer to a value or a range of values of an error rate, a reception success or a fidelity. The error tolerance bound may, for example, represent a maximum error rate in the transmission of quantum information or represent a minimum level of success of the reception of the qubits that should not be exceeded for the secure sharing of the information; otherwise, the communication may be classified as being unsecure. A low error rate may indicate a high level of accuracy in the transmitted qubits, while high reception success may indicate the ability to reliably detect and measure those qubits. For example, a higher reception success probability may indicate a lower probability of errors occurring during the transmission and measurement of qubits. Thus, a higher reception success may be associated with a lower error rate. In one example, the error tolerance bound may represent an error caused by a maximum level of eavesdropping and the noise.

[0050] The present subject matter may further use another security bound representing the eavesdropping. This security bound may be referred to as attack success bound. The attack success bound may be used to evaluate the security of the quantum communication protocol. The attack success bound may indicate the level of success of an (simulated) attack or eavesdropping by the third party. Theattack success bound may refer to a value or a range of values. The attack success bound may refer to a value or a range of values of a fidelity or of a level of success of the eavesdropping. The level of success of the attack may be evaluated using the states of intercepted qubits which are determined by the third-party quantum computing system. The determined states by the third-party quantum computing system may be compared against the prepared states of the intercepted qubits in order to evaluate the level of success of the attack. Once arrived at the receiver quantum computing system, the states of the intercepted qubits may be measured at the receiver quantum computing system, and the measured states may be compared against the prepared states of the intercepted qubits in order to evaluate the level of success of reception at the receiver quantum computing system. The level of success of the attack may be represented by the first metric. The level of success of reception may be represented by the second metric.Training the machine learning model

[0051] In one example, the machine learning model may be trained using a training dataset. The training dataset comprises multiple entries. Each entry of the entries may be associated with a given data sharing system. Each entry of the entries may comprise values of the set of parameters descriptive of the associated given data sharing system, the noise model and a label indicating the security of the given data sharing system for performing data sharing in accordance with the quantum communication protocol. An entry may for example be provided as a tuple such as: {[“values of the set of parameters”, “Noise Model”], “label”}. The noise model may indicate the noise of the noisy quantum channel of the data sharing system of the entry. The noise model may be provided as a number or other type of input whose value indicates the type of noise to which the quantum channel is exposed. In one example, the entries may comprise subsets of entries, wherein each subset of entries of the subsets may represent the respective same data sharing system which is used to share different information or share the same kind of information but at different point of times. Each pair of distinct data sharing systems which are represented in the training dataset may differ by one or more parameters of the set of parameters and / or by the noise model being used. This may provide a richtraining dataset which represents different configurations of the data sharing systems. This may enable a reliable and accurate trained model which in turns may enable secure communication of data through quantum channels.

[0052] In one example, the training dataset may be created by providing a quantum simulator to simulate different systems of sharing of data through noisy quantum channels. The quantum simulator may be used for evaluating the set of parameters for multiple simulated systems which are simulated by the quantum simulator in different noise conditions. For each simulated system, it may be determined whether the simulated system is secure or unsecure for sharing information. Each simulated system may comprise a simulated sender node and a simulated receiver node which are connected through a simulated noisy quantum channel, and a simulated third-party quantum computing system, wherein the simulated noisy quantum channel is exposed to one or more types of noises.

[0053] In one example, the determining by the quantum simulator whether the simulated system is secure or unsecure is performed by receiving an input e.g., from a user of the quantum simulator, indicating whether the simulated system is secure or not secure. That is, the user input for a given simulated system may be used as a label for the simulated system in the training dataset.

[0054] In one example, the determining by the quantum simulator whether the simulated system is secure or unsecure is performed using a security proof method. The security proof method may, for example, be executed by the quantum simulator. The security proof method comprises: determining an attack configuration for access by a third party to the noisy quantum channel of the simulated system, the attack configuration being defined by at least a quantum circuit system having specific parameters and the attack success bound, the quantum circuit system being configured to intercept a qubit on the noisy quantum channel, determine the state of the intercepted qubit without destroying it and send the qubit to the receiver node through the noisy quantum channel, defining a first metric representing a level of success of an attack by the third party and the second metric indicating a level of reception success at the receiver node; using thequantum circuit system to evaluate the first metric by at least intercepting qubits on the noisy quantum channel and using the receiver node to evaluate the second metric; determining whether the second metric fulfils the error tolerance bound and whether the first metric fulfills the attack success bound. If the second metric fulfils the error tolerance bound and the first metric fulfills the attack success bound, the simulated system is classified as being unsecure. If the second metric does not fulfil the error tolerance bound and the first metric fulfills the attack success bound, it may be determined that the simulated system is unsecure. It may be determined that the simulated system is secure if the second metric fulfills the error tolerance bound and the first metric does not fulfill the attack success bound.

[0055] The quantum circuit system that is simulated and used by the security proof method for generation of the training data may be the quantum circuit system used in the inference phase by the third party. The quantum communication protocol that is simulated and used by the security proof method for generation of the training data may be the quantum communication protocol used by the data sharing system in real time (in the inference phase).

[0056] The value of the first metric may be compared (first comparison) against the attack success bound in order to determine whether the value of the first metric fulfils the attack success bound for the simulated system. The value of the first metric fulfils the attack success bound may mean that the attack is successful. For example, he level of success of the attack fulfils the attack success bound may mean that the level of success of the attack is higher than the attack success bound e.g., fidelity metric (representing the level of success of the attack) may be higher than 80%, where 80% may be the attack success bound. The value of the second metric may be compared (second comparison) against the error tolerance bound in order to determine whether the value of the second metric fulfils the error tolerance bound for the simulated system. The value of the second metric fulfils the error tolerance bound may mean that the reception of information at the receiver node is successful (e.g., secure). For example, the level of reception success at the receiver node fulfils the error tolerance bound may mean that the level of reception success at the receiver node is higher than the error tolerance bound, wherein theerror tolerance bound may be a minimum level of success of the reception. In another example, in case the error tolerance bound is a maximum error rate, the reception error rate at the receiver node fulfills that bound if it is smaller than the error tolerance bound e.g., the error rate at the receiver node may be smaller than 10%, where 10% may be the error tolerance bound.

[0057] Thus, the security proof method may use not only the second comparison results to decide on the security of the quantum communication protocol in the simulated system, rather, it may use the results of both the first and second comparisons in order to decide on the security of the quantum communication protocol. For example, the simulated system may be classified as unsecure if the second metric fulfils the error tolerance bound and the first metric fulfills the attack success bound. In another example, the simulated system may be classified as unsecure if the second metric does not fulfil the error tolerance bound and the first metric fulfills the attack success bound. The simulated system may be classified as secure if the second metric fulfils the error tolerance bound and the first metric does not fulfill the attack success bound.

[0058] The present subject matter may thus enable two or more distant parties to communicate securely with each other. This communication may be useful in a wide range of applications where security may be critical, such as in financial transactions, government communications, and military operations.Example implementations of the security proof method

[0059] As described with the example above, the quantum simulator may be used to build the training dataset by simulating different systems and predicting their security (label) using the security proof method. The quantum simulator may, for example, be configured to simulate the quantum communication protocol using a model of a real data sharing system that enables communication of quantum information in accordance with different noise models. For example, the quantum simulator may be configured for controlling parameters for individual components and sub-protocols in the system including quantum channel and communicatingparties. The quantum simulator may, for example, be implemented as a software application.

[0060] The present subject matter may use advantageous techniques to provide different (simulated) attack configurations of the third-party quantum computing system that may enable a reliable proof of security of the quantum communication protocol using the noisy quantum channel of the simulated system. For that, one or more attack configurations may be defined using an offline analysis and the quantum simulator. The offline analysis may be referred to as an attack simulation method.

[0061] In one first optimization example, the attack simulation method may use the quantum simulator to optimize the specific parameters of the third-party quantum computing system in order to improve the attack success rate. The attack simulation method may comprise: defining a quantum circuit system comprising at least the intercepted qubit and one or more additional qubits and performing one or more quantum operations having the specific parameters, wherein the quantum operation(s) enable to determine the state of the intercepted qubit e.g., without affecting the prepared state of the intercepted qubit. The attack simulation method may further comprise the evaluation of the first metric using the determ ined / estimated states of the intercepted qubits. The attack simulation method may be repeated multiple times, wherein in each repetition, different values of the specific parameters are used. The repetition may be performed until a desired target of the first metric is reached, wherein the values of the parameters that provide the desired target are provided as optimal parameters, wherein the desired target is defined according to the noise model of the noisy quantum channel that is accessed by the third-party quantum computing system. Alternatively, the repetition may be performed for a predefined number of times, the resulting first metric values may be compared and the values of the parameters that provided the best first metric may be provided as the optimal parameters. Thus, the attack simulation method may enable to obtain optimized values of the specific parameters. These optimized values (and the associated quantum circuit system) may be used by the present security proof method in order to proof security of the sharing informationbetween the sender quantum computing system and the received quantum computing system of the simulated system. The first optimization example may be performed for different noise models. That is, the quantum circuit system may be optimized for different types of noise.

[0062] In one second optimization example, the attack simulation method may use the quantum simulator to optimize the specific parameters of the third-party quantum computing system in order to improve the attack success using machine learning. For that, an objective function may be defined. The attack simulation method may be repeated multiple times, wherein in each repetition, different values of the specific parameters are defined based on the evaluated objective function. The repetition may be performed until the objective function fulfils a convergence criterion. This example may enable an accurate determination of the optimal parameters. This may further improve the security proof according to the present subject matter. The objective function may be defined based on the type of the first metric being used and the noise model. The second optimization example may be performed for different noise models. That is, the quantum circuit system may be optimized for different types of noise.

[0063] In one example, the second metric may be a fidelity between the state of the prepared qubit as prepared by the sender node and the measured state of the qubit which is received at and measured by the receiver quantum computing system of the simulated system. The state of the prepared qubit may be represented by a density matrix p and the state measured by the receiver quantum computing system may be represented by a density matrix p2. The second metric may thus be defined as follows: F1(1,2) = ( VP1P2 P1 ■

[0064] In one example, the first metric (F2) may be the fidelity between the state of the intercepted qubit as determined or estimated by the third-party and a state of the prepared qubit as prepared by the sender node of the simulated system. The first metric may thus be defined as follows: F2

[0065] The first metric may, for example, have the value 1 , if the states are identical and the value 0, if both are orthogonal. The third-party quantum computing system of the simulated system may provide a quantum circuit system in order to keep its fidelity and the fidelity at the receiver as close to 1 as possible. In this case, the attack may only be noticed with a low probability. For example, in case the quantum communication protocol is the BB84 protocol, four different states may be selected with equal probability. In this case, the average fidelity (e.g., fidelity is measured for all different states and averaged over four distinct states) may be used as the first metric and second metric for the third-party quantum computing system and the receiver quantum computing system respectively.

[0066] In one example, the first metric used on the security proof method may be the mutual information. The mutual information may, for example, be defined as follows: where X may be the random variableassociated with bits at the sender quantum computing system and Y may be the random variable associated bits at the third-party quantum system of the simulated system, where p(x,y) is the joint probability, and p(x) and p(y) are the individual probabilities.

[0067] For example, two random bits b1 , b2 e [0, 1 ] are input for the quantum channel and the output may be the XOR value b1 ®b2. The corresponding probabilities are shown in the following table:

[0068] For example, the input 00 occurs together with the output 0 with the probability1Thus, the value of the transinformation may be 1 , e.g., out of two possible bits of information, 1 bit is transmitted through the channel. However, no information about the individual bits may have been received, because even after knowledge of b1 ®b2, the value of b1 and b2 is still equally distributed. Nevertheless, the information about the value of b1 ®b2 may be valuable for anattacker (or eavesdropper) because it may allow to restrict the search space in a brute force search of 4 possibilities to 2.

[0069] For example, the fidelity for the receiver quantum computing system of the simulated system may be referred to as F and the fidelity for the third-party quantum computing system of the simulated system may be referred to as F2. The objective function of the second optimization example may, for example, be defined as: — F2+10 x (Fx— target)2, where target is a predefined target value for the fidelity F taking into account the noise model. Alternatively, the objective function may be defined as — F2— Fr. The mutual information for the third-party quantum computing system of the simulated system may be referred to as I2. In this case, the objective function may, for example, be defined as: I2+10 x (Fx— target)2.

[0070] The first and second metrics may be evaluated using a metric determination system of the simulated system. The metric determination system may or may not be part of the third-party quantum computing system of the simulated system. For example, the metric determination system may use quantum state tomography to construct the density matrices p and p2e.g., with a series of measurements performed in different bases, and estimate the fidelity.

[0071] In one example, the quantum communication protocol may be the quantum key distribution (QKD) protocol, wherein the shared information comprises a key. The QKD protocol may, for example, be the BB84 protocol. The transmitted qubits may be photons which are prepared in computational basis states, wherein the computational basis sates may be horizontal and vertical polarization states or may be diagonal polarization states.

[0072] The present subject matter may further improve the proof of security of the quantum communication protocol using the noisy quantum channel. For that, different structures of the quantum circuit system of the third-party quantum computing system of the simulated system may be used in order to intercept the qubit and determine the state of the intercepted qubit.

[0073] In one example, different quantum circuit systems may be defined and for each quantum circuit system, the quantum circuit system may be applied in order to intercept the qubit on the quantum channel of the simulated system and evaluate the first metric. The quantum circuit system that has the best value of the first metric may be selected and used in order to perform the security proof method according to the present subject matter. Each quantum circuit system may include the intercepted qubit, a defined number of additional qubits and perform a set of quantum operations including a controlled operation and zero or more additional quantum operations. The parameters (e.g., rotation angles) of the set of quantum operations may be the specific parameters of the quantum circuit system. The number of additional qubits and additional quantum operations of each quantum circuit system may, for example, be randomly selected or may be user defined.

[0074] In one first circuit example, the quantum circuit system comprises the intercepted qubit and one or more qubits. The quantum circuit system is configured to perform a sequence of one or more quantum operations on the qubits for determining the state of the intercepted qubit without destroying the state of the intercepted qubit.

[0075] In one second circuit example, the quantum circuit system comprises the intercepted qubit and a target qubit. The target qubit is prepared in an initial basis state. In addition, the sequence of one or more quantum operations is a single quantum operation that transforms the initial basis state of the target qubit dependent on the state of the intercepted qubit without destroying the state of the intercepted qubit. The state of the intercepted qubit is determined or estimated using a state of the target qubit which is measured after application of the transformation.

[0076] In one third circuit example, the quantum communication protocol may be a QKD protocol such as BB84. According to this quantum communication protocol, the sender quantum computing system may send to the receiver quantum computing system over a classical public channel the bases that have been used to prepare the intercepted qubits. The third-party quantum computing system maybe configured to intercept communicated data over the classical public channel and have access to the bases used. The third-party quantum computing system may further be configured to save the intercepted qubits e.g., for a later operation. The attack simulation method may make use of this to control the quantum circuit system to perform a basis dependent operation using the saved qubit and information gained on the bases. For that, the quantum circuit system comprises the intercepted qubit and a target qubit. The target qubit is prepared in an initial basis state. The sequence of one or more quantum operations comprises one controlled quantum operation transforming the initial basis state of the target qubit dependent on the state of the intercepted qubit, and another quantum operation transforming the state of transformed target qubit taking into account the basis being used to prepare the intercepted qubit. The state of the intercepted qubit may be determined or estimated using a state of the target qubit which is measured after application of the two transformations without destroying the state of the intercepted qubit.

[0077] In one fourth circuit example, the quantum circuit system comprises the intercepted qubit, a first target qubit and a second target qubit. The sequence of quantum operations comprises a controlled quantum operation enabling the determination of the state of the first target qubit dependent on the state of the intercepted qubit and a quantum operation enabling the determination of the state of the second target qubit in a specific computation basis. The quantum operations may be applied by the quantum circuit system without destroying the state of the intercepted qubit.

[0078] In one fifth circuit example, the quantum circuit system may be configured to make one or more approximate state copies of the intercepted qubit. This quantum circuit system may enable to prepare a state that has as high fidelity as possible, and at the same time the fidelity for the receiver node is also preserved as well as possible. The quantum circuit system may comprise the intercepted qubit having state p and one additional qubit which may be prepared in a basis state e.g., |0 > . The quantum circuit system may be configured to perform a set of one or more quantum operations on the input state p® 10 >< 0| in order to obtain a state pwhere p is the approximate state copy of the state p of the intercepted qubit. The approximate copy p may be received at the receiver quantum computing system, but since it is an approximate copy, the fidelity at the receiver node may still be of high value. The approximate copies may be used to estimate the first metric and second metrics. The approximate copy p may be compared with the original state p in order to estimate the first metric. The approximate copy p which is received at the receiver quantum computing system may be compared with the original state p in order to estimate the second metric.

[0079] In one example, the present method may be implemented in a quantum repeater. This may enable a seamless integration of the present subject matter in existing systems.

[0080] In one example, each quantum circuit system of the above circuit examples may further be used to determine the first metric and configured to send the intercepted qubit to the receiver node through the noisy quantum channel.

[0081] The computer system according to the present subject matter may be a classical computer system or a hybrid classical quantum computer system. The computer system may be configured to control the third party and the receiver node in order to determine the values of the first and second metrics respectively. The computer system may be configured to evaluate the set of parameters other than the first and second metrics by using user input or by using the metadata file. The metric determination system of FIG. 1 provides an example of the computer system.

[0082] FIG. 1 is a diagram of a system 100 in accordance with an example of the present subject matter. The system 100 comprises a quantum communication system 110 and a metric determination system 105. The quantum communication system 110 comprises a sender quantum computing system 101 and a receiver quantum computing system 102 which are configured to exchange or share information through a noisy quantum channel 104. The quantum communication system 110 further comprises a third-party quantum computing system 103 that is configured to intercept qubits on the noisy quantum channel 104, estimate thestates of the intercepted qubits e.g., without destroying the states of the intercepted qubits and send the qubits to the receiver node 102 through the noisy quantum channel 104. For that, the third-party quantum computing system 103 may comprise a quantum circuit system which may be an experimental implementation of the schematically depicted circuit of FIGs 5B-5D and 6B. The third-party quantum computing system 103 may be located on any point of the noisy quantum channel. For example, the third-party quantum computing system 103 may be located near the receiver node 102 e.g., the third-party quantum computing system 103 may or may not be part of the receiver node 102.

[0083] The metric determination system 105 may include a classical computer or a quantum computer and communicate with components of the quantum communication system 110. The metric determination system 105 may be configured to control the operation of the third-party quantum computing system 103. The metric determination system 105 may cause the quantum circuit system of the third-party quantum computing system 103 to be used for interceptions of one or more qubits which are transmitted on the noisy quantum channel 104 and perform respective measurements to determine output information that enables to determine the metric such as the first metric. The metric determination system 105 may be configured to control the operation of the receiver node 102 in order to evaluate the second metric.

[0084] The metric determination system 105 may comprise a trained machine learning (ML) model 111. The machine learning model 111 is configured to receive as input the noise model and the values of the set of parameters which are evaluated for a given system (such as system 110), wherein the given system comprises a given receiver node (such as receiver node 102) and a given sender node (such as sender node 101 ) which are configured to share information through a given noisy quantum channel connecting the receiver node to the sender node in accordance with the quantum communication protocol and a noise model of the noise of the noisy quantum channel. FIG. 2 shows an example implementation of the machine learning model 111. The machine learning model 111 may be for example a neural network but it is not limited to. The given system may for example be a QKD system for key sharing. The input of the machine learning model 111may for example comprise L system parameters SP through SPL, fidelities F and F2of the given system and the noise model Nmindicating the noise of the noisy quantum channel. The output of the machine learning model 111 may for example be a value indicating whether the given system is secure for sharing the information or unsecure for the sharing of information. The fidelity determined for the receiver may be referred to as F and the fidelity determined for the third-party may be referred to as F2. The noise model Nm, for example, be encoded using techniques such as one-hot encoding to convert it into a numerical format that the ML model 111 can understand.

[0085] FIG. 3 is a flowchart of an example method for sharing information between a sender node and a receiver node in accordance with a quantum communication protocol. For the purpose of explanation, the method described in FIG. 3 may be implemented using the system illustrated in FIG. 1 , but is not limited to this implementation. The sender node may, for example, be the sender quantum computing system 101 and the receiver node may be the receiver quantum computing system 102.

[0086] The set of parameters may be evaluated in step 121 for the system 110 for sharing the information. In addition, the noise model of the noise of the noisy quantum channel 104 of the data sharing system may be determined e.g., in step 121. The noise model may, for example, be determined by receiving a user input indicating the noise model of the noise of the noisy quantum channel 104. Alternatively, the noise model may, for example, be determined by using a metadata file descriptive of the data sharing system 110. The system parameters of the set of parameters may, for example, be evaluated using the metadata file or by receiving user input comprising values of the system parameters. The evaluated set of parameters and the noise model indicating the noise of the noisy quantum channel 104 may be input in step 123 to the machine learning model 111. In response to the input, a prediction of the security of the system 110 may be received in step 125 from the machine learning model 111. The quantum communication protocol may be aborted in step 129 if (inquiry step 127) the system is predicted as being unsecure. The aborting may result in the shared information being not used.If the system 110 is predicted as being secure the shared information may further be used by the sender and receiver nodes.

[0087] In one example, the evaluation of the set of parameters in step 121 may comprise receiving values of the system parameters of the set of parameters and evaluating the first metric using the third-party quantum computing system and evaluating the second metric using the receiver quantum computing system. For example, the metric determination system may control the third-party quantum computing system and the receiver quantum computing system to obtain values of the density matrices which may be used to evaluate the respective fidelities. The evaluation of the set of parameters may be performed during the sharing of the information e.g., by using part of the information to be shared. Alternatively, the evaluation of the set of parameters may be performed before the sharing of said information e.g., by sharing test information.

[0088] FIG. 4 is a flowchart of a security proof method for determining whether a simulated system is secure or not secure for sharing information. The simulated system may be provided by the quantum simulator. The simulated system may, for example, be as the system illustrated in FIG. 1.

[0089] An attack configuration for access by the third party to the quantum channel may be determined in step 201. The attack configuration is defined by at least a quantum circuit system having specific parameters and an attack success bound, the quantum circuit system being configured to intercept a qubit on the quantum channel, determine the state of the intercepted qubit and send the qubit (or an approximate copy of it) to the receiver node. FIGs 5B-5D provide examples of attack configurations.

[0090] A first metric representing a level of success of an attack by the third party and a second metric indicating a level of reception success at the receiver node may be defined in step 203. For example, the first and second metrics may be user defined metrics e.g., an input may be received in step 203 which provides the definition of the first and second metrics. In another example, the first and secondmetrics may be defined by selecting them (e.g., randomly) from a list of predefined metrics.

[0091] The quantum circuit system may be used in step 205 to measure or determine the first metric by at least intercepting qubits on the quantum channel. The second metric may be evaluated in step 205 using the receiver node.

[0092] It may be determined in step 207 whether the second metric fulfils the error tolerance bound and whether the first metric fulfills the attack success bound.

[0093] If the second metric fulfils the error tolerance bound and the first metric fulfills the attack success bound, it may be determined in step 209 that the simulated system is unsecure. If the second metric does not fulfil the error tolerance bound and the first metric fulfills the attack success bound, it may be determined that the simulated system is unsecure. It may be determined (step 211 ) that the simulated system is secure if the second metric fulfills the error tolerance bound and the first metric does not fulfill the attack success bound.

[0094] Fig. 5A is a diagram representing an example quantum communication system in accordance with an example of the present subject matter. Specifically, the quantum communication system is represented by a quantum circuit 300. The quantum circuit 300 represents a qubit qO which is the qubit transmitted from the sender (Alice) 301 to the receiver (Bob) 302. The qubit qO may be intercepted by the third-party quantum computing system (Eve) 303 and used as control qubit for another qubit q1 of the quantum circuit 300. The quantum circuit 300 further shows measurement devices for measuring the qubits qO and q1 , where the qubit qO is measured at the receiver 302 and the qubit q1 is measured at the third-party quantum computing system 303. The third-party quantum computing system 303 may comprise a quantum circuit system as described with reference to FIG. 5B, 5C or 5D. The quantum circuit systems of FIGs, 5B and 5C may enable the interception of the qubit and estimation of its state without destroying or changing its state, that is, the receiver may receive the qubit as prepared by the sender.

[0095] Fig. 5B schematically depicts an example quantum circuit system 310 for the third-party quantum computing system in accordance with an example of the present subject matter. The quantum circuit system 310 may consist of a controlled rotation on Eve’s system, while Alice’s and Bob’s systems serve as the controlling system. The quantum circuit system 310 may be configured to perform a rotation along y axis on the qubit q1 using the angle a, where the angle a is the parameter of the quantum circuit system 310. The rotation may use the qubit q1 as target and the intercepted qubit qO as control qubit.

[0096] Fig. 5C schematically depicts an example quantum circuit system 311 for the third-party quantum computing system in accordance with an example of the present subject matter. The quantum circuit system 311 is an extension of the controlled rotation of quantum circuit system 310 on the Eve’s system by another, but uncontrolled operation on the Eve’s system. The quantum circuit system 311 may be configured to perform on the qubit q1 a first rotation along y axis using the angle a and using the qubit qO as control qubit, and followed by the uncontrolled rotation along the y axis using angle b, where the angles a and b are the parameters of the quantum circuit system 311 .

[0097] Fig. 5D schematically depicts an example quantum circuit system 312 for the third-party quantum computing system for the BB84 protocol in accordance with an example of the present subject matter. The quantum circuit system 312 may be configured to perform a rotation along y axis on the qubit q1 using the angle TT / 2 followed by a CNOT operation using the qubit q1 as the control qubit and qO as the target. The rotation may use the qubit q1 as target and the intercepted qubit qO as control qubit. The quantum circuit system 312 may be configured to make approximate copies of the intercepted qubit. This quantum circuit system 312 may enable to prepare a state that has as high state quality as possible with the transmitted state, so that at the same time the state quality for the receiver is also preserved as well as possible. The quantum circuit system may comprise the intercepted qubit having state p and one additional qubit which may be prepared in a basis state |0>. The quantum circuit system may be configured to perform a set of one or more quantum operations on the input state p® 10 >< 0| in order to obtaina state p®p where p is the approximate state copy of the state p of the intercepted qubit.

[0098] The copied states may be defined in a specific basis in which the original states of the transmitted qubit are defined according to the BB84 protocol. The basis states may, for example, be: Each of the copied statesmay be compared with the respective original state. The first and second metrics may be evaluated by using partial tracing of the approximate states for enabling the comparison of the approximate state at the receiver node and at the third-party with the original state of the transmitted qubit. Additionally, the approximate states which are defined in the specific basis may not be orthogonal to each other and may not be distinguished from each other without error. The Pretty Good Measurement (PGM) may, for example, be used for distinguishing the approximate states. For that, the density matrices pLwith the associated probabilities ptmay be added up to a matrix G and then the root of the pseudoinverse of G is calculated. This may provide the operators n(= ppfG^ppjG^ of a Positive Operator-Valued Measure (POVM) on the space spanned by the states. If the simulated attack has the ability to store the approximate copy of the state until Alice and Bob exchange information about the chosen basis, the third-party may perform operations on the stored state that depend on the basis. Since Bob and Eve may receive the same state, it is expected that Bob and Eve can also have the same probability of success in identifying the transferred states. In this case, the measurement may be performed in one of the two bases:fc)

[0099] In one example, if the third-party is configured to save the intercepted qubit, the simulated attack can be divided into two parts: the first part is the interaction with Alice and Bob’s system and the third-party system, which can be saved. After disclosing the selected bases, the third-party system can perform a basedependent operation on the stored qubit before measuring the qubit. This may, for example, be implemented using the circuit of FIG. 6A.

[0100] Fig. 6A is a diagram representing a quantum communication system in accordance with an example of the present subject matter. Specifically, the quantum communication system is represented by a quantum circuit 400. The quantum circuit 400 represents a qubit qO which is the qubit transmitted from the sender (Alice) 401 to the receiver (Bob) 402. The qubit qO may be intercepted by the third-party quantum computing system (Eve) 403 and used as control qubit for another qubit q1. The quantum circuit 400 further shows measurement devices for measuring the qubits qO and q1 , where the qubit qO is measured at the receiver 402 and the qubit q1 is measured at the third-party quantum computing system 403. The third-party quantum computing system 403 may comprise a first quantum circuit system as described with reference to FIG. 5B or 5C. In addition, the third- party quantum computing system 403 may comprise two second quantum circuit systems shown in FIG. 6B, each being associated with one specific basis (e.g., in case the qubits are photons the basis may comprise horizontal and vertical polarization states).

[0101] In this example, the intercepted qubit may be stored or saved by the third- part quantum computing system. In addition, the third-party quantum computing system may have access to the basis used by the sender to prepare the state of the intercepted qubit e.g., this may be the case with the BB84 protocol where the bases are sent over a classical public channel and intercepted by the third-party quantum computing system.

[0102] As indicated in FIG. 6A, the quantum circuit 400 may enable to perform a sequence of at least two operations (rotations around y axis) on the qubit q1 , e.g., the operation implemented by third-part quantum computing system 403 and operation 406. The qubit q1 is prepared in an initial basis state. The sequence of quantum operations comprises one quantum operation which is performed by the first quantum circuit system for transforming the initial basis state of the qubit q1 dependent on the state of the intercepted qubit qO. The sequence of quantum operations further comprises another quantum operation transforming the state of transformed qubit q1 taking into account the basis being used to prepare the intercepted qubit qO. This other quantum operation may be performed by one of thesecond quantum circuit systems associated with the basis used for the preparation of the intercepted qubit qO. This other quantum operation may be referred to as basis-dependent operation. As indicated in FIG. 6A, this basis-dependent operation 406 may be performed even after Bob’s system has measured the qubit qO. The state of the intercepted qubit qO may be determined by the third-party quantum computing system using a state of the qubit q1 which is measured after application of the sequence of operations.

[0103] Fig. 6B depicts an example of two quantum circuit systems 410 and 411 for the third-party quantum computing system in accordance with an example of the present subject matter. Each of the two quantum circuit systems is shown in FIG. 5C. The two quantum circuit systems may be used depending on the basis used by the Alice’s system to prepare the intercepted qubit. Since two bases may be used by the Alice’s system, these two quantum circuit systems 410 and 411 are provided to be used for the two bases respectively. For that, each of the two quantum circuit systems is configured to perform on the qubit q1 one controlled operation and a subsequent uncontrolled operation. The controlled operation in the two circuits uses the same angle a, while the uncontrolled operation uses two different angles b and c in the two quantum circuit systems.

[0104] FIG. 7 is a flowchart of a method for optimizing the parameters of the quantum circuit system in accordance with an example of the present subject matter. The parameters may be set to current values in step 501. The quantum circuit system may be used in order to measure the first metric in step 503. It may be determined in step 505 whether the first metric fulfills a convergence criterion. In case the first metric fulfills the convergence criterion, the parameter values may be provided in step 507 e.g., in order to be used in the method of FIG. 4 and FIG. 3. If the first metric does not fulfill the convergence criterion, the method goes back to step 501 for setting the parameters to other values. The convergence criterion may, for example, require the first metric to be in a target range of values, wherein the target values may be defined according to the noise model.

Claims

CLAIMS1. A method for sharing information using a data sharing system (100) comprising a sender node (101 ) and a receiver node (102) using a noisy quantum channel (104) in accordance with a quantum communication protocol, the method comprising: providing a trained machine learning model (111 ), the machine learning model being configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system in order to predict whether the given system is secure or unsecure for sharing information according to the quantum communication protocol, the set of parameters indicating a level of success of an attack by a third party and a level of reception success at a receiver node of the given system and being descriptive of the given system; determining (121 ) a noise model for a noise of the noisy quantum channel of the data sharing system; evaluating (121 ) the set of parameters for the data sharing system for sharing the information; inputting (123) the evaluated set of parameters and the noise model to the machine learning model, thereby receiving (125) a prediction of a security of the data sharing system; aborting (129) the quantum communication protocol if the data sharing system is predicted as being unsecure.

2. The method of claim 1 , wherein the noise model indicates at least one of: depolarizing channel noise, amplitude damping channel noise, phase damping channel noise or bit flip channel noise.

3. The method of claim 1 or 2, wherein the level of success of an attack is evaluated using a quantum circuit system, the quantum circuit system being configured to intercept a qubit on the noisy quantum channel and determine the state of the qubit and send the qubit through the quantum channel to the receiver node.

4. The method of claim 3, the quantum circuit system comprising the intercepted qubit and one or more qubits, the quantum circuit system being configured to perform a sequence of one or more quantum operations on the qubits for determining the state of the intercepted qubit.

5. The method of any of the preceding claims, the set of parameters comprising system parameters which are descriptive of the data sharing system, wherein the system parameters comprise at least one of: a distance between the sender and receiver nodes, a detector efficiency of a signal detector at the receiver node, design parameters of components of the data sharing system and an amount of information to be shared between the sender node and the receiver node.

6. The method of any of the preceding claims, further comprising: providing a training dataset comprising entries, each entry comprising values of the set of parameters of a given system and the noise model and a label indicating the security of the given system; training the machine learning model using the training dataset, thereby providing the trained machine learning model.

7. The method of claim 6, creating the training dataset comprising: providing a quantum simulator, the quantum simulator being configured to simulate different systems of sharing of information through quantum channels in accordance with the quantum communication protocol and different noise models; using the quantum simulator for evaluating the set of parameters for multiple systems which are simulated by the quantum simulator;for each simulated system determining whether the simulated system is secure or unsecure, thereby providing the label for the simulated system.

8. The method of claim 7, wherein the determining whether the simulated system is secure or unsecure is performed using a security proof method, the security proof method comprising: determining an attack configuration for access by a third party to the noisy quantum channel of the simulated system, the attack configuration being defined by at least a quantum circuit system having specific parameters and an attack success bound, the attack success bound being defined in accordance with the noise model, the quantum circuit system being configured to intercept a qubit on the quantum channel, and determine the state of the intercepted qubit, the quantum communication protocol requiring an error tolerance bound for the receiver node in accordance with the noise model; defining a first metric representing a level of success of an attack by the third party and a second metric indicating a level of reception success at the receiver node; using the quantum circuit system to evaluate the first metric by at least intercepting qubits on the quantum channel and using the simulated receiver node to evaluate the second metric; determining whether the second metric fulfils the error tolerance bound and whether the first metric fulfills the attack success bound; determining that the simulated system is unsecure if the second metric fulfils the error tolerance bound and the first metric fulfills the attack success bound or if the second metric does not fulfil the error tolerance bound and the first metric fulfills the attack success bound; otherwise determining that the simulated system is secure.

9. The method of any of the preceding claims, the machine learning model being a quantum machine learning model or a classical machine learning model.

10. The method of any of the preceding claims, comprising: repeatedly: preparing by the sender node a qubit in a respective basis state; sending the prepared qubit by the sender node through the quantum channel to the receiver node for enabling sharing of information; wherein the intercepted qubits which are used for evaluation of the level of success of an attack are the prepared qubits.

11. The method of any of the preceding claims, comprising: repeatedly forming an entanglement state between a sender qubit in the sender node and a receiver qubit; sending by the sender node the receiver qubit to the receiver node through the quantum channel; wherein the intercepted qubits which are used for evaluation of the level of success of an attack are the receiver qubits.

12. The method of any of the preceding claims 3 to 10, further comprising: using a quantum simulator for optimizing parameters of the quantum circuit system, the optimizing comprising repeatedly changing values of the parameters of the quantum circuit system and evaluating the first metric, the repetition being performed for obtaining a target value of the first metric; providing the specific parameters of the quantum circuit system as optimized parameters associated with the target value of the first metric.

13. The method of any of the preceding claims, the second metric being a fidelity between the state of the qubit received at the receiver node and a state of the prepared qubit, the second metric representing a level of reception success.

14. The method of any of the preceding claims, the first metric being a fidelity between the state of the intercepted qubit and a state of the prepared qubit or a mutual information between the sender node and the third party, the first metric representing the level of success of an attack.

15. The method of any of the preceding claims, wherein the quantum communication protocol is Quantum Key Distributed protocol.

16. The method of any of the preceding claims, wherein the shared information comprises an encryption key, a token, or a secret.

17. A computer program comprising instructions for causing a computer system for performing the method of claim 1 .

18. A computer system (105) for controlling a data sharing system (100) comprising a sender node (101 ) and a receiver node (102), the data sharing system being configured for information sharing using a noisy quantum channel (104) in accordance with a quantum communication protocol, the computer system (105) being configured for: providing a trained machine learning model (111 ), the machine learning model being configured to receive a noise model of noise of a noisy quantum channel of a given system and a set of parameters of the given system in order to predict whether the given system is secure or unsecure for sharing information according to the quantum communication protocol, the set of parameters indicating a level of success of an attack by a third party and a level of reception success at a receiver node of the given system and being descriptive of the given system;determining (121 ) a noise model for a noise of the noisy quantum channel of the data sharing system; evaluating (121 ) the set of parameters for the data sharing system for sharing the information; inputting (123) the evaluated set of parameters and the noise model to the machine learning model, thereby receiving (125) a prediction of a security of the data sharing system; causing (129) an abortion of the quantum communication protocol if the data sharing system is predicted as being unsecure.

19. The computer system of claim 18, being comprised in the data sharing system (100), the data sharing system comprising a quantum circuit system (310, 311 , 312) having specific parameters, the quantum circuit system being configured to intercept a qubit on the noisy quantum channel (104), determine the state of the intercepted qubit and send the qubit through the noisy quantum channel to the receiver node; the computer system (105) being configured to use the quantum circuit system to determine the level of success of an attack; the computer system (105) being configured to determine the level of reception success using the receiver node (102).

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