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

Abstract

In 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. KEYWORDS cryptography, networking, quantum cryptography, quantum key distribution, security INTRODUCTIONThe continuous-variable quantum key distribution (CVQKD) protocols 1 allow the establishment of an unconditional secure communication 2 over standard, currently established telecommunication networks. Another motivation behind the use of CVQKD is the development of the quantum Internet 10,44,58 and quantum computers 59-64 . In a CVQKD Abbreviations: AMQD, adaptive multicarrier quadrature division; AWGN, additive white Gaussian noise; BS, beam splitter

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

“…In Section 2, the notations and basic terms are summarized. For further information, see the detailed descriptions of [2][3][4][5][6][7][8][9][10].…”

“…Continuous-variable quantum key distribution (CVQKD) provides an easily implementable solution to realize unconditional secure communication over the current telecommunication networks [10][11][12][13][14][15][16][17][18][19][20][21][22]. CVQKD does not require single-photon sources and detectors and can be implemented in an experimental scenario by standard devices [1], [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], [30][31][32][33][34][35][36][37]. In a CVQKD setting, the information is carried by a continuous-variable quantum state that is defined in the phase space via the position and momentum quadratures.…”

“…In particular, the extra benefits and resources allow the realization of improved secret key rates and a higher amount of tolerable losses with unconditional security. These results also made possible to utilize several significant phenomena for CVQKD that are unavailable in a standard CVQKD protocol (such as single layer transmission [4], enhanced security thresholds [5], multidimensional manifold extraction [6], characterization of the subcarrier domain [7], adaptive quadrature detection and subchannel estimation techniques [8], extensive utilization of distribution statistics and random matrix formalism [9], and advanced statistical approaches for performance improvements [10], [41][42]).…”

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

“…Continuous-variable quantum key distribution (CVQKD) provides a method to realize unconditional secure communication over standard, currently established telecommunication networks [10][11][12][13][14][15][16][17][18][19][20][21][22]. A significant attribute of CVQKD is that, in contrast to DV (discrete variable) QKD, it does not require single-photon sources and detectors and can be implemented by standard devices [1], [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], [30][31][32][33][34][35][36][37]. In a CVQKD setting, the information is carried by a continuousvariable quantum state that is defined in the phase space via the position and momentum quadratures.…”

“…In particular, these extra benefits and resources allow the realization of higher secret key rates and a higher amount of tolerable losses with unconditional security. These innovations opened a door to the establishment of several new phenomena for CVQKD that are unrealizable in standard CVQKD, such as single layer transmission [4], enhanced security thresholds [5], multidimensional manifold extraction [6], characterization of the subcarrier domain [7], adaptive quadrature detection and sub-channel estimation techniques [8], and an extensive utilization of distribution statistics and random matrix formalism [9]. The benefits of multicarrier CVQKD have also been proposed for multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) [3].…”