Abstract
We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently-developed reliable numerical methods for key rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.
Highlights
Quantum key distribution (QKD) [1,2] enables two remote parties, Alice and Bob, to establish information theoretically secure keys even in the presence of an eavesdropper, Eve
For a given quantum key distribution (QKD) protocol, the goal of a security proof is to find a lower bound on the secure key rate
II, we review the basic steps of a QKD protocol and how the key rate can be formulated as a convex optimization
Summary
Quantum key distribution (QKD) [1,2] enables two remote parties, Alice and Bob, to establish information theoretically secure keys even in the presence of an eavesdropper, Eve. For many discrete-variable (DV) protocols, the numerical methods can be applied by using the squashing map [9,10,11] or the more general flag-state squasher [12] to reduce the problem to finite dimensions. Recent works have numerically studied asymptotic security proofs for DMCVQKD with any number of modulated states [22,23]. These approaches assume the state is finite dimensional, known as the photon-number cutoff assumption. Our method can provide a complete asymptotic security proof for discrete-modulated continuousvariable protocols with any number of modulated states, with tight key rates and without relying on the photonnumber cutoff assumption.
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