Subcarrier wave continuous variable quantum key distribution with discrete modulation: mathematical model and finite-key analysis

Abstract

In this paper we report a continuous-variable quantum key distribution protocol using multimode coherent states generated on subcarrier frequencies of the optical spectrum. We propose a coherent detection scheme where power from a carrier wave is used as a local oscillator. We compose a mathematical model of the proposed scheme and perform its security analysis in the finite-size regime using fully quantum asymptotic equipartition property technique. We calculate a lower bound on the secret key rate for the system under the assumption that the quantum channel noise is negligible compared to detector dark counts, and an eavesdropper is restricted to collective attacks. Our calculation shows that the current realistic system implementation would allow distributing secret keys over channels with losses up to 9 dB. Quantum key distribution (QKD) is a method of sharing symmetric cryptographic keys between two parties that is based on encoding information in the states of quantum objects and subsequent distillation of the key through a classic communication channel. The first quantum cryptography protocols exploited the quantum system with degrees of freedoms 1-3. A numerous amount of different techniques for security proofs for discrete variable QKD systems has already been presented 4-13. Experimental implementations of this family of QKD protocols rely on single-photon detectors for quantum state measurements. In turn, continuous-variable QKD (CV-QKD), which was proposed later, relies on methods of coherent detection, homodyne or heterodyne, for gaining information about the quantum states. In other words, single-photon detection is replaced by conventional optical communication methods. However, security proofs for CV-QKD protocols currently remain less advanced 14,15. There are two types of CV protocols that differ by signal modulation method: Gaussian 16,17 , where the complex amplitudes of coherent states are selected randomly from a normal distribution, and discrete modulation (DM) 18-22 with weak coherent phase-coded states. Other CV-QKD protocols are based on two-mode squeezed vacuum states transmission and measurement via homodyne or heterodyne detection 23. Security proofs for Gaussian CV-QKD protocols remain the most developed: they were presented against general attacks in the finite key regime using several different approaches 24. Security analysis for CV-QKD protocol with two-mode squeezed vacuum states was also performed 25,26. Discrete-variable CV-QKD protocols possess several important advantages; among those are relative implementation simplicity and a possibility to minimize the number of parameters that need to be monitored. Nevertheless, security proofs for discrete-modulation CV-QKD systems require special consideration. In the asymptotic limit, its security has been proven against collective attacks 27. Recently it was shown that security proof for CV-QKD with discrete modulation against general attacks is possible 27. Here we propose an implementation of CV-QKD protocol based on subcarrier wa...

Finite-size security of continuous-variable quantum key distribution with digital signal processing

“…The other branch gives priority to simplicity of the modulation and uses a very small (usually two to four) number of amplitudes [25][26][27][28] . As for the security analysis, the status is more or less similar to the Gaussian constellation case, and current security proofs are either in the asymptotic regime against collective attacks [29][30][31][32] or in the finite-size regime but against more restrictive attacks 33,34 . Hence, regardless of approaches, a complete security proof of CV QKD in the finite-size regime against general attacks has been a crucial step yet to be achieved.…”

Coherent detection schemes for subcarrier wave continuous variable quantum key distribution

“…The mathematical model presented in this subsection describes the classic case as the most understandable. A similar model in terms of quantum mechanics, which is more justified for the description of QKD systems, is presented in [26].…”

“…Due to the active development of novel QKD systems using non-standard states of light there is a necessity to upgrade existing detection schemes. The subcarrier wave (SCW) QKD [19,20,21,22,23,24,25,26] is striking example of such a system. A defining property of subcarrier wave QKD is the method for quantum state encoding.…”

Heterodyne-based subcarrier wave quantum cryptography under the chromatic dispersion impact

“…In SCW QKD protocols [15][16][17][18][19][20] multimode weak coherent states are generated by electro-optic phase modulation. As a result, sideband spectrum is formed with its phase, relative to the initial carrier field, containing the quantum information [21][22][23] (detailed descriptions of SCW DV-QKD and CV-QKD protocols can be found in [15] and [20], respectively). The main advantages of SCW QKD are the simplification of the phase shift matching between Alice and Bob and lack of complex interference schemes and efficient usage of the channel's bandwidth.…”