Methods and systems for quantum-classical communication

Abstract

Disclosed is a method for simultaneous quantum-classical communication (SQCC). The method comprises encoding a signal with combined classical-quantum information using a polarization encoding to encode both a classical component of the combined classical-quantum information and a quantum component of the combined classical- quantum information. The method further comprises transmitting the encoded signal over a communication medium.

Description

"Methods and systems for quantum-classical communication" Cross-reference

[0001] The present application claims priority from United States of America Provisional Patent Application 63 / 697,349 filed on 20 September 2024, the contents of which are incorporated herein by reference in their entirety. Technical Field

[0002] This disclosure relates to methods and systems for combined quantum- classical communication, also referred to as simultaneous quantum-classical communication (SQCC), and in particular SQCC for free-space optical (FSO) applications. Background

[0003] Classical communication systems are used to exchange digital information via the transmission of data through various communication media, such as optical fibers, radio waves, and copper wires. These systems encode information into electromagnetic signals, which are then transmitted over a communications medium to a receiver. The receiver decodes the signals back into the original information. Classical communication has been the backbone of global connectivity, enabling the transfer of information across applications ranging from voice calls to internet data exchanges.

[0004] As the volume of data transmitted over communication networks continues to grow exponentially, there is an increasing need to enhance both the throughput and security of data transmission. High throughput ensures that large amounts of data can be transmitted quickly and efficiently, which is crucial for applications such as streaming services, cloud computing, and real-time data analytics. Security, on the other hand, is paramount to protect sensitive information from unauthorized access andcyber threats. Traditional encryption methods are becoming increasingly vulnerable to sophisticated attacks, necessitating the development of more robust security measures.

[0005] Quantum communication offers a promising means to address the limitations of classical communication systems. By leveraging the principles of quantum mechanics quantum communication can achieve a level of information security beyond that which can be provided by a classical protocol. Quantum key distribution (QKD), for example, allows for the creation of cryptographic keys that are theoretically immune to eavesdropping. Additionally, quantum communication can potentially enhance the throughput of data transmission by enabling faster and more efficient processing of information.

[0006] The integration of quantum and classical systems, such as to enable combined quantum-classical communication, is referred to as “simultaneous quantum-classical communication” (SQCC). SQCC allows for the transmission of classical information and quantum information (e.g., QKD) together over the same medium, enhancing efficiency and reducing costs. SQCC is advantageous in its ability to leverage existing communication systems with minimal modifications, making it a practical solution for enhancing security and data.

[0007] Continuous-Variable Quantum Key Distribution (CV-QKD) is an example of a quantum communication approach in the optical domain that is suited to SQCC. Unlike traditional QKD methods that use discrete variables, CV-QKD utilizes continuous variables, such as the quadratures of the electromagnetic field, to encode information. This approach allows CV-QKD to be implemented using existing optical communication infrastructures and components. Note, henceforth we use the phrase CV-QKD encoding to refer to any form of CV encoding, not necessarily the form of encoding just for a specific application such as QKD.

[0008] Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission thatany or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application.

[0009] Throughout this specification the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps. Summary

[0010] There is provided a method for simultaneous quantum-classical communication (SQCC), the method comprising: encoding a signal with combined classical-quantum information using a polarization encoding to encode both a classical component of the combined classical-quantum information and a quantum component of the combined classical-quantum information; and transmitting the encoded signal over a communication medium.

[0011] In some embodiments, the polarization encoding is based on a plurality of Stokes operators.

[0012] In some embodiments, the encoded signal comprises an optical beam.

[0013] In some embodiments, the polarization encoding comprises modulating a Stokes operator associated with the classical component by mapping a classical bit to a direction of polarization of the optical beam.

[0014] In some embodiments, the optical beam is generated as a controlled combination of a plurality of polarized optical beams.

[0015] In some embodiments, the plurality of polarized optical beams comprises two polarized optical beams with equal amplitude and prepared in respective H and V directions of polarization.

[0016] In some embodiments, the polarization encoding comprises encoding the quantum component with a continuous variable Quantum Key Distribution (CV-QKD) encoding.

[0017] In some embodiments, the CV-QKD encoding comprises modulating a set of Stokes operators associated with the quantum component.

[0018] In some embodiments, the set of Stokes operators associated with the quantum component includes first and second operators whose normalized versions resemble the conjugate field quadratures used for quantum encoding in coherent-state CV-QKD.

[0019] In some embodiments, the polarization encoding comprises using: a magneto- optic modulator (MOM) to couple the Stokes operator associated with the classical component to the first Stokes operator associated with the quantum component; and an electro-optic modulator (EOM) to couple the Stokes operator associated with the classical component to the second Stokes operator associated with the quantum component.

[0020] In some embodiments, the first and second Stokes operators associated with the quantum component are modulated independently and according to a Gaussian distribution.

[0021] In some embodiments, the encoded optical beam is transmitted through a free- space optical (FSO) communication medium.

[0022] There is also provided a method for simultaneous quantum-classical communication (SQCC), the method comprising: receiving a signal transmitted over a communication medium, wherein the received signal is encoded with combined classical-quantum information using a polarization encoding to encode both a classical component of the combined classical-quantum information and a quantum component of the combined classical-quantum information; and decoding the combined classical- quantum information of the received signal.

[0023] In some embodiments, the polarization encoding is based on a plurality of Stokes operators.

[0024] In some embodiments, the received signal comprises an encoded optical beam.

[0025] In some embodiments, decoding the combined classical-quantum information of the received signal comprises: splitting the encoded optical beam into a transmitted portion and a reflected portion; and decoding the classical component and the quantum component of the signal by detecting an intensity of the respective transmitted and reflected portions of the encoded optical beam.

[0026] In some embodiments, decoding the classical component of the signal comprises: applying the transmitted portion of the encoded beam to a polarizing beam splitter; and detecting an intensity of each output of the polarizing beam splitter to measure a Stokes operator associated with the classical component.

[0027] In some embodiments, decoding the quantum component of the signal comprises randomly switching between measurement of one or more Stokes operators associated with the quantum component, wherein the measurement comprises: applying the reflected portion of the encoded beam to at least a half-wave plate, and then to a polarizing beam splitter; and detecting an intensity of each output of the polarizing beam splitter to measure the respective one of the one or more Stokes operators associated with the quantum component.

[0028] In some embodiments, decoding the quantum component of the combined classical-quantum signal comprises normalizing the measurements of each of the one or more Stokes operators associated with the quantum component by the measurement of the Stokes operator associated with the classical component.

[0029] There is also provided a system for simultaneous quantum-classical communication (SQCC), the system comprising a transmitter, wherein the transmitter is configured to: encode a signal with combined classical-quantum information using apolarization encoding to encode both a classical component of the combined classical- quantum information and a quantum component of the combined classical-quantum information; and transmit the encoded signal over a communication medium.

[0030] In some embodiments, the transmitter further comprises a magneto-optic modulator (MOM) and an electro-optic modulator (EOM), and wherein using the polarization encoding comprises using: the magneto-optic modulator (MOM) to couple the Stokes operator associated with the classical component to the first Stokes operator associated with the quantum component; and the electro-optic modulator (EOM) to couple the Stokes operator associated with the classical component to the second Stokes operator associated with the quantum component.

[0031] In some embodiments, the transmitter is further configured to modulate the first and second Stokes operators associated with the quantum component independently and according to a Gaussian distribution.

[0032] In some embodiments, the transmitter is further configured to transmit the encoded optical beam through a free-space optical (FSO) communication medium.

[0033] In some embodiments, the system further comprises a receiver configured to: receive the optical beam from the communication medium; and decode the combined classical-quantum signal by: splitting, via a beam splitter of the receiver, the encoded optical beam into a transmitted portion and a reflected portion; and decoding the classical component and the quantum component of the combined classical-quantum signal by detecting an intensity of the respective transmitted and reflected portions of the encoded optical beam.

[0034] In some embodiments, decoding the classical component of the combined classical-quantum signal comprises: applying the transmitted portion of the encoded beam to a polarizing beam splitter of the receiver; and detecting an intensity of each output of the polarizing beam splitter to measure a Stokes operator associated with the classical component.

[0035] In some embodiments, decoding the quantum component of the combined classical-quantum signal comprises randomly switching between measurement of one or more Stokes operators associated with the quantum component, wherein the measurement comprises: applying the reflected portion of the encoded beam to at least a half-wave plate, and then to a polarizing beam splitter; and detecting an intensity of each output of the polarizing beam splitter to measure the respective one of the one or more Stokes operators associated with the quantum component.

[0036] In some embodiments, the receiver further comprises an optical switch, and the receiver is configured to operate the optical switch to direct the reflected portion of the encoded beam in accordance with the random switching between the measurement of the one or more Stokes operators associated with the quantum component. In some embodiments, the aforementioned optical switch can be replaced by a beam splitter with a fixed or tunable transmittance, and the receiver is configured to measure the Stokes operators associated with the quantum component simultaneously. Brief Description of Drawings

[0037] Some embodiments of the invention will now be described with reference to the accompanying drawings, in which:

[0038] Fig.1 is a schematic diagram of a communication system for performing SQCC, according to some embodiments;

[0039] Fig.2a is a block diagram of the communication system of Fig.1 configured for performing Stokes-based encoding and decoding, according to some embodiments;

[0040] Fig.2b is an exemplary implementation of the communication system of Fig. 2a;

[0041] Fig.3a is a flow diagram of a method for using polarization-based SQCC to encode and transmit a combined signal, as performed by the communication system, according to some embodiments;

[0042] Fig.3b is a flow diagram of a method for using Stokes-based SQCC to encode and transmit a combined signal, as performed by the communication system, according to some embodiments;

[0043] Fig.4a is a flow diagram of a method for performing a classical encoding step of the method for SQCC of Fig.3b;

[0044] Fig.4b is a flow diagram of a method for performing a quantum encoding step of the method for SQCC of Fig.3b;

[0045] Fig.5a is a flow diagram of a method for using polarization-based SQCC to decode a combined signal as performed by the communication system, according to some embodiments;

[0046] Fig.5b is a flow diagram of a method for using Stokes-based SQCC to decode a combined signal as performed by the communication system, according to some embodiments;

[0047] Fig.6a is a flow diagram of a method for performing a classical decoding step of the method for SQCC of Fig.5b;

[0048] Fig.6b is a flow diagram of a method for performing a quantum decoding step of the method for SQCC of Fig.5b; and

[0049] Fig.7 is a flow diagram of a method for performing polarization-based SQCC, according to some embodiments.Description of Embodiments

[0050] Conventional approaches to SQCC typically transmit classical information using parameters such as the arrival time of coherent states, while quantum information is distributed through the quadrature components of these states. Integration is achieved through techniques such as multiparameter modulation, which combines different modulation schemes for classical and quantum data.

[0051] Accordingly, the practical implementation of SQCC presents several challenges. First, there is a need for a local oscillator (LO) for the measurement of quadratures at the receiver. In SQCC over FSO channels, such a LO is usually sent from the transmitter to the receiver along with the classical-quantum signal (via some multiplexing schemes) to establish a phase reference for detecting quantum signals. The use of a co-propagating LO increases the likelihood of a successful eavesdropping attack, compromising the unconditional information security promised by the quantum component, such as QKD (see, for example, [1] and [2]). Despite recent efforts to address the aforementioned security issue by generating a local LO (LLO) at the receiver (e.g., as described in [3] and [4]), the current demonstrations are mostly restricted to controlled environments (e.g., optical fibers as described in [5], [6] and [7]) where phase noise introduced by the atmosphere is absent.

[0052] One approach to address the need for a LO in the context of a pure quantum communication approach, such as CV-QKD, is to use the quantum polarization properties of intense light fields. The feasibility of polarization-encoded CV-QKD has been confirmed via experimental demonstrations (see, e.g., [8], [9],

[0010] ,

[0011] ,

[0012] ). This eliminates the need for sending a separate LO and allows for the simple readout of quantum information based on direct detection (e.g., via standard photodiodes).

[0053] However, unlike in a pure quantum communication approach, conventional SQCC has the additional issue of experiencing an undesirable interplay (manifesting in the form of, e.g., crosstalk) between the quantum and classical components of the combined signal, which results in degraded performance (e.g., see

[0013] and

[0014] ). Thisis one factor preventing or limiting conventional SQCC from providing utility in the context of a practical deployment.

[0054] Accordingly, to improve upon conventional SQCC, it is necessary to address both the need for a LO for the quantum communication, and the existence of crosstalk between the classical and quantum components. These two effects are interrelated and will depend on the encoding applied to both the classical and quantum components, particularly in optical implementations where the components are encoded into the same optical beam. It is desired to develop systems and methods that address these problems, or that at least provide a useful alternative. Overview

[0055] Disclosed herein are systems and methods for simultaneous quantum- classical communication (SQCC) using polarization encoding to encode, on a common signal, both a classical component and a quantum component of a combined classical- quantum signal. The encoded optical beam is transmitted over a communication medium, where a received signal may be measured to retrieve information of the classical and quantum components of the combined classical-quantum signal by utilizing the Stokes operators.

[0056] Fig.1 schematically illustrates a communication system 100 for implementing the proposed SQCC techniques, which are referred to as polarization–based SQCC. The communication system 100 comprises: a transmitter 102; and a receiver 106 communicatively coupled to the transmitter 102 via a communication medium 120. In some examples, communication medium 120 is configured to permit optical communication (e.g., via an optical beam) between the transmitter 102 and the receiver 106, and may comprise a satellite-based FSO channel.

[0057] In one implementation of the proposed technology, the polarization encoding is performed via Stokes operators (referred to as Stokes-based SQCC). Transmitter 102 comprises an encoder 104 configured to utilize Stokes operators, or variants of the same, to encode a signal with combined classical-quantum information (referred to asthe “combined classical-quantum signal”, or as the “combined signal” for brevity herein), by encoding both a classical component of the combined classical-quantum information and a quantum component of the combined classical-quantum information, and to transmit the encoded (combined) signal to the receiver 106 via the communication medium 120. In some examples, the encoded signal comprises an optical beam (i.e., as prepared by the encoder 104). The encoder 104 utilizes a plurality of Stokes operators which are each associated with either the classical component, or the quantum component, of the combined signal for the purpose of acting as a carrier for the information of the respective component in the transmitted signal (e.g., via the optical beam).

[0058] The receiver 106 comprises a decoder 108 configured to perform decoding of the combined signal. In some examples, the decoder 108 is configured to recover the classical and quantum components of the combined signal encoded by the encoder 104 without a separate LO signal, and based on measurements of the intensity of the received optical beam. Although the communication system 100 depicted in Fig.1 comprises the transmitter 102 and the receiver 106, in other configurations the communication system 100 may comprise only a transmitter 102 or only a receiver 106, for example where an external system is configured to either receive and decode the combined signal associated with the transmitted encoded optical beam, or to encode and transmit the same respectively.

[0059] In some examples described herein, the single Stokes operator ^^^^is used to encode the classical component, while the two Stokes operators ^^^ଶand ^^^ଷare used to encode the quantum component according to CV-QKD. However, it will be appreciated that other encodings exist for a quantum component that is based on a different form of QKD, and where the encoding may comprise a different number and / or combination of the Stokes operators, or other polarization parameters. Examples of other such SQCC techniques using polarization-based encodings are discussed herein below (e.g., with reference to Fig.7).

[0060] The proposed polarization-based SQCC systems and methods provide advantages over conventional SQCC, including at least: (i) eliminating the need for a separate local oscillator to decode the classical and quantum components of the encoded combined signal; (ii) enhancing the separation of the classical and quantum signal components by reducing cross-contamination during encoding and decoding, for example by the modulation of the operators; and (iii) allowing for the simple and efficient readout of both quantum and classical information from the respective components of the combined signal by performing direct detection of the optical beam. Polarization-based SQCC using Stokes operators

[0061] Using the H (horizontal) and the ^^ (vertical) directions as a basis, a transverse electromagnetic field can be arbitrarily decomposed into two components corresponding to orthogonal polarization modes.

[0062] Consider three common decompositions that describe the same transverse electromagnetic field with ^^ and ^^ components, diagonal (^^) and anti-diagonal (^^) components, and right-handed circular (^^) and left-handed circular (^^) components. As a result, the polarization state of a beam of light can be described using the four Stokes parameters, namely, ^^^(the total intensity of the ^^ and ^^ components), ^^^(the intensity difference between the ^^ and ^^ components), ^^ଶ(the intensity difference between ^^ and ^^ components), and ^^ଷ(the intensity difference between ^^ and ^^ components).

[0063] In quantum optics, after changing intensities to photon-number operators, the corresponding Stokes operators are given by

[0015] :where aˆ( a ˆ † ) denotes the annihilation (creation) operator, and ^^^ denotes the photon-number operator.

[0064] Note that, in Eqs. (1)-(4), and the subscripts of the operators denote the above-defined polarization components. The Stokes operator ^^^ commutes with the otherthree Stokes ope ˆ ˆ ^rators, that is [S 0 , Si ]^ 0 ( i ^ 1,2,3) . The commutator of the remainingthree Stokes operators is given by ^^^^^ , ^^^^൧ = 2^^^^^^^^^^^ (^^, ^^, ^^ = 1,2,3), leading to thecorresponding uncertainty relations Var൫^^^^൯Var൫^^^^൯ ≥ ห^^^^^^^^^^^หଶ (withVarˆ ˆ being the variance of each Stokes operator). This dictates that itis not possible to simultaneously measure any two of the Stokes operators with certainty as long as the third one is non-zero.

[0065] In Eqs. (1)-(4), the annihilation and creation operators can be expressed asa ˆM ^^ M ^ ^ a ˆ M ( M ^ { H , V }) where αெ is the classical amplitude and δ^^^ெ representsthe quantum fluctuation of the ^^ component with [^aˆM , ^ a ˆ M † ]^ 1 and ^ ^ a ˆ M ^ ^ 0. As aresult, Eqs. (1)-(4) can be re-expressed as ˆˆ

[0066] Note that in deriving Eqs.(5)-(8) αெis treated as a real number, and only the first-order fluctuation terms are considered. The variance of the Stokes operators is then given byˆ ˆ ˆ ˆ ˆ

[0067] The sections below outline the use of the Stokes operators for the proposed encoding, which is based on the use of strongly polarized optical beams. Specifically,for classical encoding the Stokes operator ^^^^ is modulated by mapping a binaryclassical bit to the dominating direction of polarization (either ^^ or ^^) of an optical beam. Encoder 104 encodes bit “1” (“0”) by setting|^^ு ଶ ≫ |^^ |ଶ ≈ 0 (|^^ |ଶ|ଶ ) ^Sˆ ^ ^ |^ | 2 ( ^ ˆ 2|≫ ˆ^ˆ ^^^ு|≈ 0 , leading to 1 H S 1 ^ ^ ^ | ^ V | ) and^ S 1 ^ ^ ^ S 0 ^ . For QKDencoding, the Stokes operators ^^^ and ^^^ are modulated, and the normalized Stokeso ˆ2 ˆ ˆ ଶ ଷperators S ^ ^ S 2 / ^ S 1 ^ 1 / 2 and Sˆ3 ^ ^ S ˆ 3 / ^ S ˆ 1 ^ 1 / 2 satisfy= 2^^ and thus resemblethe conjugate field quadratures (i.e., ^^^ and ^^^) used for quantum encoding in CV-QKD.System model

[0068] In the proposed Stokes-based SQCC, the Stokes operators are utilized ascarriers of classical information component (i.e., via ^^^ ) and the quantum informationcomponent (i.e., ^^^ଶ , ^^ ^^ଷ for quantum communications using CV-QKD) of the encodedcombined signal.

[0069] Fig.2a illustrates communication system 100 configured for performing Stokes-based encoding and decoding according to some examples described herein. Transmitter 102 comprises optics unit 202 configured to generate or receive an optical beam for encoding the combined signal. Encoder 104 performs Stokes-based polarization encoding via a classical encoding unit 103 and a quantum encoding unit 105.

[0070] Classical encoding unit 103 comprises at least an optical attenuator 204 configured to attenuate an input optical beam received from optics unit 202. In someexamples, the classical encoding unit 103 further comprises one or more other modules, such as a beam splitter 206. The classical encoding unit 103 generates the classical component of the combined signal on an optical beam output by the unit 103, for example by operating the attenuator 204 to form a controlled combination of a plurality of polarized optical beams.

[0071] Quantum encoding unit 105 comprises a magneto-optic modulator (MOM) 208 and an electro-optic modulator (EOM) 210 configured to receive the optical beam with the classical component encoded, and to subsequently encode the quantum component of the combined signal. We note that within the quantum encoding unit 105 additional optical elements may be included (not all shown here for simplicity), such as a half-wave plate (HWP). In one embodiment the beam entering unit 105 first passes through an HWP, then through an EOM, then an MOM, then through two HWPs. The settings of the HWPs are dependent on the classical information being encoded. The transmitter 102 encodes an input information signal IN into a combined signal for transmission over the communication medium 120 by operating the encoding units 103, 105, as described below.

[0072] The receiver 106 comprises a classical decoder unit 230, a quantum decoder unit 250, and one or more other components (e.g., a beam splitter 212, and a switch 214) configured to collectively operate on the encoded optical beam received from the communication medium 120. In some examples, receiver 106 comprises a post- processing unit 220 configured to receive output from each of the classical and quantum decoder units 230, 250 and to generate the output information signal OUT.

[0073] Fig.2b schematically illustrates an exemplary implementation of the communication system 100 of Fig.2a.

[0074] Fig.3a illustrates a method 300’ performed by the system 100 to encode (at step 302’) and transmit (at step 304’) a combined signal using polarization-based SQCC.

[0075] Fig.3b illustrates a method 300 performed by the system 100 to encode and transmit a combined signal using Stokes-based SQCC, according to the implementations depicted in Figs.2a and 2b. The steps of method 300 are described in the following sections. We note that within the blocks shown in Figs 2a and 2b additional optical elements may be included (not all shown here for simplicity), such as a quarter-wave plate (QWP) and / or a half-wave plate (HWP). Initial state preparation

[0076] At step 302, the Stokes-based SQCC commences with the preparation of the optical beam. The transmitter 102 performs the initial preparation of the unmodulated state. Then, at step 304 the transmitter 102 performs the classical encoding of the combined signal.

[0077] Fig.4a illustrates a method for performing the classical encoding according to the Stokes-based SQCC of method 300. At step 402, for each shot of classical-quantum modulation, the transmitter 102, via optics unit 202, prepares two classical beams, one being polarized in ^^ direction and the other in ^^ direction, with the same classical amplitude α. In practice, there is some practical energy constraint limiting α so the classical communication is not completely error free (as discussed below).

[0078] At step 404, the optics unit 202 ensures that the two beams are distinguishable only in their polarization and directs them to the beam splitter (BS) 206 with a variable transmittance τ. Other means of preparing a beam comprising the mixed polarization states are available. These include separately modulating the intensity of the polarized beams and then combining them via some device (such as a fixed-transmittance beam splitter). Classical encoding

[0079] At step 406, the transmitter 102 performs a mapping of the classical bit onto the output beam by performing a controlled combination of the polarized beams. The combining of the two prepared polarized beams is performed at the BS 206. In thisexample, the controlled combining is achieved by an electronically controlled variable optical attenuator, such as attenuator 204. In other examples, a wavelength-independent tunable directional coupler may be used (e.g., the 2x2 coupler circuit described in

[0016] ).

[0080] Specifically, to encode classical bit “0” (“1”'), the transmitter 102 adjusts ^^ to^^ ∼ 0 (^^ ∼ 1), making the output beam (emerging from the transmission port of theBS) strongly polarized in ^^-direction (^^-direction) and weakly polarized in ^^-direction (^^-direction). At this stage, the state of the output beam can be considered as a two- mode coherent state.

[0081] To elaborate further, consider a scenario where transmitter 102 encodes theclassical bit “1” by setting τ ∼ 1, leading to |αு|ଶ = |α|ଶ ≫ |α^|ଶ ≈ 0. The Stokesoperators in Eqs. (5)-(8) then become ˆˆ ˆ

[0082] Since the beam is strongly polarized along the ^^-direction, the second term ofEq. (13) can be neglected. After a further normalization of ^^^ଶ and ^^^ଷ , Eqs. (13)-(14)become ˆ

[0083] Similarly, if the transmitter 102 encodes ``0'', then τ ∼ 0 to give |α^|ଶ=|α|ଶ ≫ |αு|ଶ ≈ 0, resultingˆ ˆ Notethat, the subscript (^ ) vac indicates that unmodulated ^^^ଶᇱ and ^^^ଶᇱ have zero mean andvariance equals to that of vacuum fluctuations.Quantum encoding

[0084] With reference to Fig.3, at step 306 the transmitter 102 performs the quantum encoding of the combined signal. Fig.4b illustrates a method for performing the quantum encoding according to the Stokes-based SQCC of method 300. At steps 412 and 414, the transmitter 102 operates the quantum encoding unit 105, which comprises a QKD modulator consisting of an MOM 208 and an EOM 210 in this example. TheMOM 208 introduces a controlled weak coupling from ^^^^ to ^^^ଶ (while keeping ^^^u c a g d , n t e O i t ^ ଷn h n e ) a d h E M n roduces a controlled weak coupling from to ^^ (while^ଷkeeping ^^ଶ unchanged).

[0085] In some embodiments, three auxiliary HWPs, HWP1, HWP2, and HWP3 are configured dynamically according to the encoded classical bit. The beam passes first through HWP1, then the EOM, then the MOM, then HWP2, and then HWP3. When a classical bit "1" is encoded, HWP1 and HWP2 are positioned at an angle of 22.5º, and HWP3 is positioned at an angle of 0º. When classical bit "0" is encoded, HWP1 and HWP2 are positioned at an angle of 67.5º, and HWP3 is positioned at an angle of 90º. The operation of the wave plates can be equivalently achieved using one or more non- adjusted passive optical devices and / or reconfigurable active optical devices (e.g., Pockels cell) controlled by properly designed control signals according to the specific quantum modulation format and / or classical modulation format.

[0086] For each shot, the transmitter modulates ^^^ଶ (^^^ଷ ) with a small random realnumber via the MOM 208 (EOM 210), effectively adding a small fluctuation termunmodulated ^^^ଶᇱ (^^^ଷ ) in Eq. (16) (Eq.(17)).

[0087] By controlling the modulation current through a coil of the MOM 208(modulation voltage applied to the EOM 210), ^X M ^,QKDˆ) can be adjusted continuously according to the random number. Specifically, the modulation current through the MOM 208 and modulation voltage applied to the EOM 210 are adjustedsuch that the small QKD modulations ^Xˆ M ^,QKD and ^Xˆ M^,QKDare independent andfollow a Gaussian distribution with zero mean and the quantummodulation, the modulated ^^^ଶᇱ and ^^^ଷᇱ becomeˆ ˆ ˆ ˆ

[0088] The variance of the modulated ^^^ଶᇱ and ^^^ଷᇱ then becomeVar(Sˆ 2 ^ )^ Var( S ˆ 3 ^ ) ^ 1 ^ V mod. (20)Transmission

[0089] With reference to Fig.3, at step 308 the transmitter 102 transmits the optical beam (which can be considered to be in a two-mode coherent state) to the receiver 106, or another external system, via communication medium 120. In this example, the communication medium 120 is a FSO channel with transmissivity ^^, given asT ^10 ^ L 10, where L is the channel loss in dB. In some examples, the transmitter 102 isimplemented as a satellite transmitting to a ground receiver 106, which can be approximated as a downlink channel that is diffraction dominated (i.e., fixed ^^ predominantly set by the transceiver aperture sizes; see the numerical phase-screen simulations of

[0017] ).

[0090] Fig.5a illustrates a method 500’ performed by the system 100 to receive (at step 502’) and decode (at step 504’) a combined signal using polarization-based SQCC.

[0091] Fig.5b illustrates a method 500 performed by the system 100 to decode a received combined signal using Stokes-based SQCC, according to the implementation depicted in Figs.2a and 2b. The steps of method 500 are described in the following sections.Classical decoding

[0092] At step 502, receiver 106 receives the encoded optical beam from the communication medium 120. To commence the decoding the receiver 106 first splits the received beam into a transmitted and reflected portions using a beam splitter (BS1) 212 with transmittance η (i.e. at step 504).

[0093] At step 506, the receiver 106 decodes the classical component from the transmitted portion of the beam. Fig.6a illustrates a method for performing the classical decoding according to the Stokes-based SQCC of method 500.

[0094] In order to determine the encoded classical bit, at step 602 the receiver 106 directs the transmitted component of BS1 into the classical decoding module 230, which splits its input using a polarizing beam splitter (PBS).

[0095] At step 604, the classical decoding module 230 performs a direct detection of intensity of each of the two PBS outputs using a photodetector (e.g., photodiode), and then takes the difference between the measurement results. This operation effectivelymeasures ^^^^ = ^^^ு −in Eq. (2), which is the Stokes operator associated with theclassical component (i.e., the carrier of the classical information in the combinedsignal). If the measured result ofis positive, the classical decoding unit 130 decodesthe classical bit as “1” (recall Eq. (15)), and if the measured result of ^^^^ is negative, itwill decode the classical bit as “0”. The classical decoding unit 130 is configured tostore or buffer the measurement result of ^^^^ for the later steps.

[0096] The bit error rate (BER) at the receiver 106 may be used as a performance metric for classical communications. A bit error happens when the transmitter 102 transmits classical bit “0” (“1”) and the receiver 106 receives “1” (“0”) from the classical decoding of step 506.

[0097] There are at least two sources of noise that affect the transfer of the classical bit, namely, the vacuum noise, and the electronic noise νel. The BER for the classical communication part of Stokes-based SQCC is given bywhere ^^ = 1 / 4, ^^ =and erfc(^ ) denotes the complementary error

[0098] Unlike the conventional SQCC (where the QKD modulation imposes a noise- like effect on the decoding of classical information

[0014] ), in the proposed Stokes-basedSQCC approach the Gaussian modulation of ^^^ଶ and ^^^ଷ (used for QKD encoding) do notcontribute to any noise in the decoding of the classical bit. This is due to the careful design of the classical and quantum encoding steps.

[0099] For example, the classical encoding ensures that classical amplitudes αுand α^cannot be both non-zero at the same time, and the quantum encoding ensures that the zero-mean quantum modulation is always applied to the weakly polarizedcomponent whose classical amplitude is zero. Such a design ensures both ^^^^^ ^ andVar(S 1 )̂ do not depend on the quantum modulation, eliminating any potentialinterference imposed by the quantum modulation on the decoding of the classical bit. Quantum decoding

[0100] With reference to Fig.5, at step 508 the receiver 106 decodes the quantum component from the reflected portion of the beam. Fig.6b illustrates a method for performing the quantum decoding according to the Stokes-based SQCC of method 500.

[0101] To perform quantum decoding, the receiver 106 operates the quantumdecoding unit 250, which performs a measurement of ^^^ଶ and ^^^ଷ followed by anormalization.

[0102] At step 606, the receiver 106 uses an optical switch 214 that randomly directs the reflected component of BS1212 towards a respective measurement circuit (asshown in Fig.2b) for the measurement of ^^^ଶ or ^^^ଷ . At step 608, the quantum decodingunit 250 applies the reflected portion of the beam to at least a half-wave plate, and then to a polarizing beam splitter (PBS) of the respective measurement circuit. Then, at step 610, as for the classical decoding step 506, the quantum decoding unit 250 performs a detection based on the intensity of the beam (e.g., via photodiodes).

[0103] Specifically, in the measurement circuit used to measure ^^^ଶ , the quantumdecoding unit 250 directs the reflected component of BS1212 through a half-wave plate (HWP) positioned at 22.5∘, followed by a decoding sub-module to measure the difference between the number of photons in the ^^ (diagonal) component (i.e., ^^^^) and the ^^ (anti-diagonal) component (i.e., ^^^^).

[0104] Similarly, in the measurement circuit used to measure ^^^ଷ , the quantumdecoding unit 250 directs the reflected component of BS1212 through an HWP at an angle of 22.5∘, a quarter-wave plate (QWP) at 45∘, and then to a decoding sub-module to determine the difference between the numbers of photons in the ^^ (right-handed circular) component (^^^ோ) and the ^^ (left-handed circular) component (^^^^).

[0105] The quantum decoding unit 250 normalizes the measurement results of ^^^ and^^^ଷ y h r c r e m a u e v l ^ ଶb t e e o d d e s r d a ue of ^^^ (with channel transmissivity ^^ and thetran ^sᇱmittance ^^ of BS1212 taken into account), and the receiver 106 extracts the values of ^^ଶ and ^^^ଷᇱ associated with the quantum component of the combined signal.

[0106] The quantum decoding unit 250 may repeat steps 606 to 608 as the switch 214 randomly switches between measurement of the Stokes operators associated with thequantum component (i.e., ^^^ଶ , ^^^ଷ ). The optical switch 214 can also be replaced by abeam splitter with a fixed or tunable transmittance, allowing the quantum decoding unit 250 to measure the Stokes operators associated with the quantum component simultaneously.

[0107] In some examples, the receiver 106 operates the post-processing unit 220 to perform one or more post-processing operations on the measured classical and / or quantum component values, including for example sifting, parameter estimation,information reconciliation (e.g., reverse reconciliation), and privacy amplification, which may enhance the security of a final secret key (e.g., against eavesdropping). Interference effects

[0108] The performance of SQCC is dependent on the degree of interference imparted by the classical component of the combined signal to the quantum component of the signal during encoding by the transmitter 102, and as measured following decoding at the receiver 106. That is, a bit error in classical decoding negatively impacts the quantum component of the combined signal via the introduction of an additional noise, which thereby provides a means to measure the performance of the proposed SQCC.

[0109] A bit error happens during the classical decoding performed by the receiver106 (i.e., at step 506) when the measured value of ^^^^ differs by a sign from what thetransmitter 102 prepared (i.e., at step 304) and transmitted (at step 308). By using such an incorrect result in the normalization, the receiver 106 effectively adds a phase flip of −π / 2 to the extracted values of ^^^ଶᇱ and ^^^ଷᇱ .

[0110] For example, if the transmitter 102 tries to convey the classical bit “1” (bysetting ^^^^ = |αு|ଶ = |α|ଶ) but the receiver 106 incorrectly decodes a “0” bit, thereceiver 106 will use −|α^|ଶ = −|α|ଶ for the normalization step, resulting in a −π / 2phase between the determined values of ^^^ଶᇱ and ^^^ଷᇱ and their corresponding originalvalues that the transmitter 102 intended to encode for QKD.

[0111] In conventional SQCC (as described in

[0013] and

[0014] ), the performance of CV- QKD is heavily limited by the phase instability noise, which is proportional to the power allocated to the classical part of the communication. However, advantageously this type of noise does not exist in the proposed polarization-based SQCC techniques, including, for example, Stokes-based SQCC, since it does not require the use of aᇱᇱ^ ^ and ^^ are retrieved by normalizing theseparate LO. Instead, the values of ^^ଶ ଷ^ ^ measured values of ^^ and ^^ by a function of the measured value of the Stokesଶ ଷ^ operator in post-processing. The classical information carried by ^^ co-propagates^with the quantum information over the communications medium 120. Since ^^^^effectively behaves analogously to a “local oscillator (LO)", there is no requirement fora separate LO to conduct measurements on ^^^ଶ and ^^^ଷ in the proposed techniques.

[0112] In some examples, high-sensitivity photodetectors may be used in both classical decoding unit 230 and the quantum decoding unit 250 to further improve the robustness of the direct detection performed by the same.

[0113] The secret key rate is used as the performance metric of the QKD part of the Stokes-based SQCC. The noise sources affecting this part include: the total channel- added noise Ξch= ^ି்+ ξ + ^^ (where ξ is the overall excess noise and ^^ =4^^ ^^ / ^^ is the additional noise term resulted from classical bit errors) and thedetmeocdtorB-EaRdded^noise Ξdet = (1 − η + νel) / η . The total noise affecting the quantumcommunication is given by Ξtot = Ξchconnecting the BER to the QKD.

[0114] Although the QKD part the Stokes-based SQCC is described as a prepare-and- measurement scheme, the performance of the technique can be analysed using the equivalent entanglement-based description. Since ^^^ଶᇱ (^^^ଷᇱ ) is equivalent to the fieldquadrature ^^^ (^^^) in conventional CV-QKD, a virtual two-mode-squeezed vacuum(TMSV) state can be established with covariance matrix (CM)where A (B) denotes the index of the first (second) mode, V ^Var^ ^ Var( S ˆ 3 ^ )which is given by Eq. (20), ^z ^ diag(1, ^ 1) , andI 2 ^ diag(1,1) .

[0115] In the entanglement-based description, mode B of the TMSV state is sent through the FSO channel from the transmitter 102 to the receiver 106. Taking intoaccount the channel loss and all the aforementioned noise terms, the CM of the resulting two-mode state is given by

[0116] It is assumed that a hypothetical attacker (e.g. an eavesdropper) does not have control over νeland η since both of them are inside the receiver 106. The secret key rate of the QKD part of the Stokes-based SQCC is given by

[0018] :where β is the reconciliation efficiency, χEBis the Holevo information between the receiver 106 and the attacker, and ^^ABis the mutual information between the transmitter 102 and the receiver 106, which is given by

[0117] Assuming that the attacker applies a collective attack (i.e., the same attack is applied to all quantum states and an optimal collective measurement is performed on them at any later time), the Holevo information between the receiver 106 and the attacker is given by

[0118] According to

[0013] , λ^,ଶ,ଷ,ସin Eq. (26) are given by

[0120] Using Eqs. (27)-(28), the value of χBEis calculated via Eq. (26) to obtain the secret key rate expressed in Eq. (24).

[0121] It will be appreciated that other means exist for determining the equations that dictate a secret key rate, especially when finite-length keys are considered. The proposed polarization-based SQCC can readily accommodate these different means of estimating the secret key rate. The secret key rate can also be qualified by adding a probability of failure of the QKD protocol (or other probabilities or indications that the secret key may not be secure). The proposed polarization-based SQCC techniques can also readily accommodate such qualifiers to the secret key.

[0122] It will be appreciated that other means exist for determining the equations and error rates used in the analysis, including classical bit error rates. Different analyses could include different noise models, different mathematical assumptions, and different mathematical approximations than those described here.General polarization-based SQCC

[0123] In addition to the examples presented herein for Stokes-based SQCC, other examples of the system 100 exist for performing the proposed polarization-based SQCC.

[0124] Fig.7 illustrates a method 700 performed by the system 100 to perform polarization-based SQCC. Those ordinarily skilled in the art will recognize the devices and equipment that are required in order to deploy the examples described with reference to the method 700, and where those devices reside in the system 100. In some examples, the elements of system 100 as implemented to perform the method 700 may be connected to a wider communication system, computer interface, or other means of control, that can monitor and set appropriate parameters and settings if appropriate or useful to do so.

[0125] With reference to Fig.7, at step 702 one or more components the system 100 create or obtain a signal to be used as a carrier of the communication (referred to as a source signal). In some examples, the source signal is a light beam consisting of photons.

[0126] At step 704, one or more components of the system 100 perform the encoding of the classical and quantum information. This may be done by embedding polarization parameters onto the same common signal. The common signal may be formed on an optical beam, for example by modulating the number of photons in a specific polarization mode across several different polarization modes, or by changing some other parameter in the different polarization modes such as the quadrature values. The encoding may use all polarization modes available, or a subset of them. The system 100 may be configured to perform encoding of the classical information before, after, or simultaneously with the encoding of the quantum information.

[0127] In some examples, the system 100 may be configured to utilize one or more polarization parameters to perform the encoding, such as for example the Stokes parameters. The system 100 may be configured to vary the functional form of thepolarization parameters, for example to utilize scaled, transformed, or otherwise modified versions of the parameters, and / or different combinations of the polarization parameters or any one or more modified versions of the same, to encode the combined classical and quantum information.

[0128] Additionally, the system 100 may be configured to use different forms of hardware to encode the classical and quantum information such as, but not limited to, electro optical modulators, wave plates, beam splitters, polarizers, polarizing beam splitters, attenuators, amplifiers, intensity detectors, homodyne detectors, heterodyne detectors, and wavelength filters. Settings of the hardware could be controlled manually and / or electronically, and be done locally and / or remotely.

[0129] At step 706, the system 100 transmits the signal that contains both the classical and quantum information to a receiver.

[0130] At step 708, the signal that contains both the classical and quantum information is received by the receiver.

[0131] At step 710, the signal is processed to decode the classical and quantum information. In some examples, the system 100 is configured to perform decoding of the received signal by measuring the number of photons in a specific polarization mode across several different polarization modes, or by measuring some other parameter in the different polarization modes such as the quadrature values. The system 100 may be configured to perform decoding of the classical information before, after, or simultaneously with the decoding of the quantum information.

[0132] In some examples, the system 100 is configured to decode the received signal on arrival at the receiver or to store the signal in classical memory, quantum memory, or both, at the receiver prior to processing.

[0133] In some examples, the system 100 is configured to processes the signal using one or more intermediate devices within the communication channel 120. For example,loss compensation and / or error correcting techniques may be applied to the signal before and / or during transmission and / or on or shortly following receipt.

[0134] In some examples, the system 100 is configured to perform one or more types of signal pre-processing or post-processing as part of the encoding 704 and / or decoding 710. Each respective step may involve the system 100 invoking classical or quantum coders or decoders (as appropriate) at a transmitter and / or a receiver of the system 100, as implemented as software and / or hardware. Exemplary classical encoders may include low-density parity check matrix codes, turbo-codes or other encoders. Exemplary quantum coders and decoders may perform one or more quantum error- correcting techniques.

[0135] In some examples, the system 100 is configured to utilize other QKD protocols to achieve the combined classical quantum communication whilst still using the same encoded parameters as described herein. Examples include device- independent QKD, measurement-device independent QKD, and twin-field QKD.

[0136] In some examples, the system 100 is configured to use a vacuum signal as part of the combined signal or encoded information (noting that in quantum mechanics the vacuum is not empty). Alternatively, or in addition, the system 100 may use a combination of discrete variable QKD and continuous variable QKD to perform the quantum encoding step.

[0137] For example, the system 100 may comprise one or more additional measurement devices configured to separate incoming signals including the separation of discrete variable signals and continuous variable signals at the receiver, such as additional polarized beam splitters. The discrete variable information may be embedded in single photons that form part of a larger photon ensemble that comprises the signal.

[0138] In some examples, the encoded signal is part of a larger Hilbert space, some of which is inaccessible to the system 100 according to some configurations. In some examples, the encoded signal is part of a larger entangled quantum state, some of whichis inaccessible to the system 100 according to some configurations. Further, in some examples, a portion of the received signal may be removed or missing, which may occur as a result of processing of the signal with a device such as a beam splitter. System 100 may be configured to treat this portion of the signal separately (e.g. to measure then discard it). In some examples, the system 100 comprises one or more quantum repeater components (e.g. which are configured to act on the signal between the transmission and reception steps).

[0139] In some examples, the system 100 is configured for integration with other systems and components, such as but not limited to machine learning and / or channel estimation modules implementing corresponding algorithms or tools. The system 100 may be configured to integrate with devices that form a wider communication network, such as a quantum computer network. Such a network may be terrestrial based, satellite based or some combination of both.

[0140] In some examples, the system 100, and any integrated components or systems, is configured for SQCC using one or more of free space, underwater, and fiber-based communication channels. The range of communication frequencies for transmission of the combined signal may include optical, terahertz and radio frequencies depending on the form or properties of the channels. In some examples, the system 100 is configured to utilize multi-antenna technology, multi-beam technology, multi-transmitters, and multi-receivers for the communication of the combined signal over the one or more channels.

[0141] Exemplary applications of performing SQCC with the system 100 may include quantum key distribution, quantum teleportation, quantum sensing, and other applications that use classical and quantum information. In some examples, the system 100 is configured to perform post-quantum cryptography solutions as an additional layer of security. Such solutions may be added to the classical communication alone, the quantum communication alone, or both. In some examples, the system 100 is configured to be used for only classical or only quantum communication by discarding some information at the receiver. For example, the receiver may be configured so as toonly have the ability to decode the classical communication alone, the quantum communication alone, or both.

[0142] It will be appreciated by persons skilled in the art that numerous variations and / or modifications may be made to the above-described embodiments, without departing from the broad general scope of the present disclosure. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive. References [1] X.-C. Ma et al., “Local oscillator fluctuation opens a loophole for Eve in practical CV QKD systems,” Phys. Rev. A, vol.88, p.022339, 2013. [2] J.-Z. Huang et al., “Quantum hacking on quantum key distribution using homodyne detection,” Phys. Rev. A, vol.89, p.032304, 2014. [3] D. Huang et al., “High-speed continuous-variable QKD without sending a local oscillator,” Opt. Lett., vol.40, pp.3695–3698, 2015. [4] A. Marie and R. Alléaume, “Self-coherent phase reference sharing for CV QKD,” Phys. Rev. A, vol.95, p.012316, 2017. [5] B. Qi et al., “Generating the local oscillator “locally” in CV QKD based on coherent detection,” Phys. Rev. X, vol.5, p.041009, 2015. [6] D. B. S. Soh et al., “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X, vol.5, p.041010, 2015. [7] T. Wang et al., “Pilot-multiplexed CV quantum key distribution with a real local oscillator,” Phys. Rev. A, vol.97, p.012310, 2018.[8] S. Lorenz, N. Korolkova, and G. Leuchs, “Continuous-variable quantum key distribution using polarization encoding and post selection,” Appl. Phys. B, vol. 79, pp.273–277, 2004. [9] Z. Zheng et al., “Performance analys. of QKD using polarized coherentstates in free-space channel,” Chin. Phys. B, vol.32, p.030306, 2023.

[0010] D. Elser et al., “Feasibility of free space QKD with coherent polarization states,” New J. Phys., vol.11, p.045014, 2009.

[0011] B. Heim et al., “Atmospheric continuous-variable quantum communication,” New J. Phys., vol.16, p.113018, 2014.

[0012] S.-Y. Shen et al., “Free-space CV QKD of unidimensional Gaussian modulation using polarized coherent states in an urban environment,” Phys. Rev. A, vol.100, p.012325, 2019.

[0013] B. Qi, “Simultaneous classical communication and QKD using continuous variables,” Phys. Rev. A, vol.94, p.042340, 2016.

[0014] B. Qi and C. C. W. Lim, “Noise analysis of simultaneous quantum key distribution and classical communication scheme using a true local oscillator,” Phys. Rev. Appl., vol.9, p.054008, 2018.

[0015] N. Korolkova et al., “Polarization squeezing and continuous-variable polarization entanglement,” Phys. Rev. A, vol.65, p.052306, 2002.

[0016] M. Wang et al., “Tolerant, broadband tunable 2 x 2 coupler circuit,” Opt. Express, vol.28, pp.5555–5566, 2020.

[0017] M. S. Winnel et al., “Classical-quantum dual encoding for laser communications in space,” New J. Phys., vol.26, p.033012, 2024.

[0018] F. Grosshans et al., “Quantum key distribution using Gaussian modulated coherent states,” Nature, vol.421, pp.238–241, 2003.

Claims

CLAIMS:

1. A method for simultaneous quantum-classical communication (SQCC), the method comprising: encoding a signal with combined classical-quantum information using a polarization encoding to encode both a classical component of the combined classical- quantum information and a quantum component of the combined classical-quantum information; and transmitting the encoded signal over a communication medium.

2. The method of claim 1, wherein the polarization encoding is based on a plurality of Stokes operators.

3. The method of claim 2, wherein the encoded signal comprises an optical beam.

4. The method of claim 3, wherein the polarization encoding comprises modulating a Stokes operator associated with the classical component by mapping a classical bit to a direction of polarization of the optical beam.

5. The method of claim 4, wherein the optical beam is generated as a controlled combination of a plurality of polarized optical beams.

6. The method of claim 5, wherein the plurality of polarized optical beams comprises two polarized optical beams with equal amplitude and prepared in respective H and V directions of polarization.

7. The method of any of claims 4 to 6, wherein the polarization encoding comprises encoding the quantum component with a continuous variable Quantum Key Distribution (CV-QKD) encoding.

8. The method of claim 7, wherein the CV-QKD encoding comprises modulating a set of Stokes operators associated with the quantum component.

9. The method of claim 8, wherein the set of Stokes operators associated with the quantum component includes first and second operators whose normalized versions resemble the conjugate field quadratures used for quantum encoding in coherent-state CV-QKD.

10. The method of claim 9, wherein the polarization encoding comprises using: a magneto-optic modulator (MOM) to couple the Stokes operator associated with the classical component to the first Stokes operator associated with the quantum component; and an electro-optic modulator (EOM) to couple the Stokes operator associated with the classical component to the second Stokes operator associated with the quantum component .

11. The method of claim 10, wherein the first and second Stokes operators associated with the quantum component are modulated independently and according to a Gaussian distribution.

12. The method of any of claims 3 to 11, wherein the encoded optical beam is transmitted through a free-space optical (FSO) communication medium.

13. A method for simultaneous quantum-classical communication (SQCC), the method comprising: receiving a signal transmitted over a communication medium, wherein the received signal is encoded with combined classical-quantum information using a polarization encoding to encode both a classical component of the combined classical-quantum information and a quantum component of the combined classical-quantum information; anddecoding the combined classical-quantum information of the received signal.

14. The method of claim 13, wherein the polarization encoding is based on a plurality of Stokes operators.

15. The method of claim 14, wherein the received signal comprises an encoded optical beam.

16. The method of claim 15, wherein decoding the combined classical-quantum information of the received signal comprises: splitting the encoded optical beam into a transmitted portion and a reflected portion; and decoding the classical component and the quantum component of the signal by detecting an intensity of the respective transmitted and reflected portions of the encoded optical beam.

17. The method of claim 16, wherein decoding the classical component of the signal comprises: applying the transmitted portion of the encoded beam to a polarizing beam splitter; and detecting an intensity of each output of the polarizing beam splitter to measure a Stokes operator associated with the classical component.

18. The method of claim 17, wherein decoding the quantum component of the signal comprises randomly switching between measurement of one or more Stokes operators associated with the quantum component, wherein the measurement comprises:applying the reflected portion of the encoded beam to at least a half-wave plate, and then to a polarizing beam splitter; and detecting an intensity of each output of the polarizing beam splitter to measure the respective one of the one or more Stokes operators associated with the quantum component.

19. The method of claim 18, wherein decoding the quantum component of the combined classical-quantum signal comprises normalizing the measurements of each of the one or more Stokes operators associated with the quantum component by the measurement of the Stokes operator associated with the classical component.

20. A system for simultaneous quantum-classical communication (SQCC), the system comprising a transmitter, wherein the transmitter is configured to: encode a signal with combined classical-quantum information using a polarization encoding to encode both a classical component of the combined classical- quantum information and a quantum component of the combined classical-quantum information; and transmit the encoded signal over a communication medium.

21. The system of claim 20, wherein the polarization encoding is based on a plurality of Stokes operators.

22. The system of claim 21, wherein the encoded signal comprises an optical beam.

23. The system of claim 22, wherein using the polarization encoding comprises modulating a Stokes operator associated with the classical component by mapping a classical bit to a direction of polarization of the optical beam.

24. The system of claim 23, wherein the transmitter is configured to generate the optical beam as a controlled combination of a plurality of polarized optical beams.

25. The system of claim 24, wherein the plurality of polarized optical beams comprises two polarized optical beams with equal amplitude and prepared in respective H and V directions of polarization.

26. The system of any of claims 23 to 25, wherein using the polarization encoding comprises encoding the quantum component using a continuous variable Quantum Key Distribution (CV-QKD) encoding.

27. The system of claim 26, wherein using the CV-QKD encoding comprises modulating a set of Stokes operators associated with the quantum component.

28. The system of claim 27, wherein the set of Stokes operators associated with the quantum component includes first and second operators whose normalized versions resemble the conjugate field quadratures used for quantum encoding in coherent-state CV-QKD.

29. The system of claim 28, wherein the transmitter further comprises a magneto- optic modulator (MOM) and an electro-optic modulator (EOM), and wherein using the polarization encoding comprises using: the magneto-optic modulator (MOM) to couple the Stokes operator associated with the classical component to the first Stokes operator associated with the quantum component ; and the electro-optic modulator (EOM) to couple the Stokes operator associated with the classical component to the second Stokes operator associated with the quantum component.

30. The system of claim 29, wherein the transmitter is further configured to modulate the first and second Stokes operators associated with the quantum component independently and according to a Gaussian distribution.

31. The system of any of claims 22 to 30, wherein the transmitter is further configured to transmit the encoded optical beam through a free-space optical (FSO) communication medium.

32. The system of any of claims 22 to 31, wherein the system further comprises a receiver configured to: receive the optical beam from the communication medium; and decode the combined classical-quantum signal by: splitting, via a beam splitter of the receiver, the encoded optical beam into a transmitted portion and a reflected portion; and decoding the classical component and the quantum component of the combined classical-quantum signal by detecting an intensity of the respective transmitted and reflected portions of the encoded optical beam.

33. The system of claim 32, wherein decoding the classical component of the combined classical-quantum signal comprises: applying the transmitted portion of the encoded beam to a polarizing beam splitter of the receiver; and detecting an intensity of each output of the polarizing beam splitter to measure a Stokes operator associated with the classical component.

34. The system of claim 33, wherein decoding the quantum component of the combined classical-quantum signal comprises randomly switching between measurement of one or more Stokes operators associated with the quantum component, wherein the measurement comprises:applying the reflected portion of the encoded beam to at least a half-wave plate, and then to a polarizing beam splitter; and detecting an intensity of each output of the polarizing beam splitter to measure the respective one of the one or more Stokes operators associated with the quantum component.

35. The system of claim 34, wherein the receiver further comprises an optical switch, and wherein the receiver is configured to operate the optical switch to direct the reflected portion of the encoded beam in accordance with the random switching between the measurement of the one or more Stokes operators associated with the quantum component.

36. The system of any of claims 34 to 35, wherein decoding the quantum component of the combined classical-quantum signal comprises normalizing the measurements of each of the one or more Stokes operators associated with the quantum component by the measurement of the Stokes operator associated with the classical component.

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