Abstract
Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.
Highlights
Quantum key distribution (QKD) [1,2] is an important cryptographic primitive in the era of quantum technology, since it enables two honest parties, traditionally known as Alice and Bob, to establish information-theoretically secure keys against any eavesdropper (Eve) who is bound by the laws of quantum mechanics
There are plenty of QKD protocols, which can be categorized into two families according to their detection technology: discrete variable (DV) and continuous variable (CV)
When we prove the security of a prepareand-measure scheme, we apply the source-replacement scheme [26,27,28,29] to obtain an equivalent entanglementbased scheme and prove the security of the entanglementbased scheme, which is easier to analyze
Summary
Quantum key distribution (QKD) [1,2] is an important cryptographic primitive in the era of quantum technology, since it enables two honest parties, traditionally known as Alice and Bob, to establish information-theoretically secure keys against any eavesdropper (Eve) who is bound by the laws of quantum mechanics. We noticed an independent work [18] that analyzes the asymptotic security of the quaternary modulation scheme with heterodyne detection In this security analysis [18], Ghorai et al use a reduction to the Gaussian optimality proof method and apply a semidefinite program (SDP) technique with a photon-number cutoff assumption. [23] to prove the security against collective attacks in the asymptotic limit Another contribution of this work is that we further develop the framework to handle the classical postprocessing for the numerical method presented in Ref. We present a complete framework for postprocessing in Appendix A
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