Multicarrier Continuous-variable Quantum Key Distribution Research Articles

Performance analysis for OFDM-based multi-carrier continuous-variable quantum key distribution with an arbitrary modulation protocol.

Multi-carrier continuous-variable quantum key distribution (CV-QKD) is considered to be a promising way to boost the secret key rate (SKR) over the existing single-carrier CV-QKD scheme. However, the extra excess noise induced in the imperfect multi-carrier quantum state preparation process of N subcarriers will limit the performance of the system. Here, a systematic modulation noise model is proposed for the multi-carrier CV-QKD based on the orthogonal frequency division multiplexing (OFDM). Subsequently, the performance of multi-carrier CV-QKD with arbitrary modulation protocol (e.g. QPSK, 256QAM and Gaussian modulation protocol) can be quantitatively evaluated by combining the security analysis method of the single-carrier CV-QKD. Under practical system parameters, the simulation results show that the SKR of the multi-carrier CV-QKD can still be significantly improved by increasing the carrier number N even with imperfect practical modulations. Specifically, the total SKR of multi-carrier CV-QKD can be optimized by carefully choosing N. The proposed model provides a feasible theoretical framework for the future multi-carrier CV-QKD experimental implementation.

Order statistics and random matrix theory of multicarrier continuous‐variable quantum key distribution

SummaryIn a multicarrier continuous‐variable quantum key distribution (CVQKD) protocol, the information is granulated into Gaussian subcarrier CVs and the physical Gaussian link is divided into Gaussian sub‐channels. Here, we propose a combined mathematical framework of order statistics and random matrix theory for multicarrier continuous‐variable quantum key distribution. The analysis covers the study of the distribution of the sub‐channel transmittance coefficients in the presence of a Gaussian noise and the utilization of the moment generation function (MGF) in the error analysis. We reveal the mathematical formalism of sub‐channel selection and formulation of the transmittance coefficients and show a reduced complexity progressive sub‐channel scanning method. We define a framework to evaluate the statistical properties of the information flowing processes in multicarrier CVQKD protocols. Using random matrix theory, we express the achievable secret key rates and study the efficiency of the adaptive multicarrier quadrature division‐multiuser quadrature allocation (AMQD‐MQA) multiple‐access multicarrier CVQKD. The proposed combined framework is particularly convenient for the characterization of the physical processes of experimental multicarrier CVQKD.

Multicarrier continuous-variable quantum key distribution

The multicarrier continuous-variable quantum key distribution (CVQKD) protocol is defined. In a CVQKD protocol, the information is conveyed by coherent quantum states. The quantum continuous variables are sent through a noisy quantum channel. For a quantum channel with additive-multiplicative noise both additive and multiplicative disturbances are present in the transmission. The multiplicative disturbance is an inherent attribute of diverse physical environments. Physical links with additive and multiplicative disturbances can represent a more general approach than purely additive noise links in several practical scenarios. In a standard CVQKD setting, the noise is modeled as an additive white Gaussian noise caused by an eavesdropper (Gaussian quantum link). As a corollary, standard CVQKD protocols are not optimal for arbitrary Gaussian quantum channels if multiplicative disturbances are also present in the physical link. Here, we define the adaptive multicarrier quadrature division (AMQD) modulation technique for CVQKD. The AMQD method is optimal for arbitrary Gaussian quantum channels with arbitrary multiplicative disturbances. The protocol granulates the Gaussian random input into Gaussian subcarrier continuous variables in the encoding phase, which are then decoded by a continuous unitary transformation. The subcarrier coherent variables formulate sub-channels from the physical link which leads to improved transmission efficiency, higher tolerable loss, and excess noise in comparison to standard CVQKD protocols. We also derive the security proof of multicarrier CVQKD at optimal Gaussian attacks in the finite-size and asymptotic regimes.

Subcarrier Domain of Multicarrier Continuous-Variable Quantum Key Distribution

The subcarrier domain of multicarrier continuous-variable quantum key distribution (CVQKD) is defined. In a multicarrier CVQKD scheme, the information is granulated into Gaussian subcarrier CVs and the physical Gaussian link is divided into Gaussian sub-channels. The subcarrier domain injects physical attributes to the description of the subcarrier transmission. We prove that the subcarrier domain is a natural representation of the subcarrier-level transmission in a multicarrier CVQKD scheme. We also extend the subcarrier domain to a multiple-access multicarrier CVQKD setting. We demonstrate the results through the adaptive multicarrier quadrature-division (AMQD) CVQKD scheme and the AMQD-MQA (multiuser quadrature allocation) multiple-access multicarrier scheme. The subcarrier domain representation provides a general apparatus that can be utilized for an arbitrary multicarrier CVQKD scenario.

Secret Key Rate Adaption for Multicarrier Continuous-Variable Quantum Key Distribution

A multicarrier continuous-variable quantum key distribution (CVQKD) protocol uses Gaussian subcarrier quantum continuous variables (CVs) for the transmission. Here, we define an iterative error-minimizing secret key adaption method for multicarrier CVQKD. The proposed method allows for the parties to reach a given target secret key rate with minimized error rate through the Gaussian sub-channels by a sub-channel adaption procedure. The adaption algorithm iteratively determines the optimal transmit conditions to achieve the target secret key rate and the minimal error rate over the sub-channels. The solution requires no complex calculations or computational tools, allowing for easy implementation for experimental scenarios.

Statistical quadrature evolution by inference for multicarrier continuous-variable quantum key distribution

We define the statistical quadrature evolution (QE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol uses Gaussian subcarrier quantum continuous variables for information transmission. The QE scheme utilizes the theory of mathematical statistics and statistical information processing. The QE model is based on the Gaussian quadrature inference (GQI) framework to provide a minimal error estimate of the CV state quadratures. The QE method evaluates a unique and stable estimation of the non-observable continuous input from the measurement results and through the statistical inference method yielded from the GQI framework. We prove that the QE method minimizes the overall expected error by an estimator function and provides a viable, easily implementable, and computationally efficient way to maximize the extractable information from the observed data. The QE framework can be established in an arbitrary CVQKD protocol and measurement setting and is implementable by standard low-complexity functions, which is particularly convenient for experimental CVQKD.

Singular value decomposition assisted multicarrier continuous-variable quantum key distribution

We define the singular value decomposition (SVD) assisted multicarrier continuous-variable quantum key distribution (CVQKD) protocol. The proposed protocol uses the singular value decomposition of the Gaussian quantum channel, which yields an additional degree of freedom for the phase space transmission. This additional degree of freedom can further be exploited in a multiple-access scenario. The SVD-assistance defines the eigenchannels of the Gaussian physical link, which can be used for the simultaneous reliable transmission of multiple user data streams. Our transmission model also includes the singular interference avoider (SIA) precoding scheme. The proposed SIA precoding scheme prevents the eigenchannel interference to reach an optimal transmission over a Gaussian link. We demonstrate the results through the adaptive multicarrier quadrature division–multiuser quadrature allocation (AMQD-MQA) CVQKD multiple-access scheme. The singular value assisted transmission provides improved simultaneous transmission rates for the users, particularly in crucial low signal-to-noise ratio regimes.

Diversity space of multicarrier continuous‐variable quantum key distribution

SummaryThe diversity space of multicarrier continuous‐variable quantum key distribution (CVQKD) is defined. The diversity space utilizes the resources that are injected into the transmission by the additional degrees of freedom of the multicarrier modulation. We prove that the exploitable extra degree of freedom in a multicarrier CVQKD scenario significantly extends the possibilities of single‐carrier CVQKD. The manifold extraction allows for the parties to reach decreased error probabilities by utilizing those extra resources of a multicarrier transmission that are not available in a single‐carrier CVQKD setting. We define the multidimensional manifold space of multicarrier CVQKD and the optimal tradeoff between the available degrees of freedom of the multicarrier transmission. We extend the manifold extraction for the multiple‐access AMQD‐MQA (multiuser quadrature allocation) multicarrier protocol. The additional resources of multicarrier CVQKD allow the achievement of significant performance improvements that are particularly crucial in an experimental scenario.

Gaussian quadrature inference for multicarrier continuous-variable quantum key distribution

A multicarrier continuous-variable quantum key distribution (CVQKD) protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. Here, we propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and implementable by standard low-complexity statistical functions.

Multiple access multicarrier continuous-variable quantum key distribution

One of the most important practical realizations of the fundamentals of quantum mechanics is continuous-variable quantum key distribution (CVQKD). Here we propose the adaptive multicarrier quadrature division–multiuser quadrature allocation (AMQD–MQA) multiple access technique for continuous-variable quantum key distribution. The MQA scheme is based on the AMQD modulation, which granulates the inputs of the users into Gaussian subcarrier continuous-variables (CVs). In an AMQD–MQA multiple access scenario, the simultaneous reliable transmission of the users is handled by the dynamic allocation of the Gaussian subcarrier CVs. We propose two different settings of AMQD–MQA for multiple input-multiple output communication. We introduce a rate-selection strategy that tunes the modulation variances and allocates adaptively the quadratures of the users over the sub-channels. We also prove the rate formulas if only partial channel side information is available for the users of the sub-channel conditions. We show a technique for the compensation of a nonideal Gaussian input modulation, which allows the users to overwhelm the modulation imperfections to reach optimal capacity-achieving communication over the Gaussian sub-channels. We investigate the diversity amplification of the sub-channel transmittance coefficients and reveal that a strong diversity can be exploited by opportunistic Gaussian modulation.