Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks

Abstract

We give an achievable secret key rate of a binary modulated continuous variable quantum key distribution schemes in the collective attack scenario considering quantum channels that impose arbitrary noise on the exchanged signals. Bob performs homodyne measurements on the received states and the two honest parties employ a reverse reconciliation procedure in the classical postprocessing step of the protocol.

Security of Continuous-Variable Quantum Key Distribution Against General Attacks

“…One can see from Figure 5 that the two-state protocol can only work in a regime where the excess noise is very small: around 1/1000. We note that this result is compatible with the results obtained in [22] where the authors study the security of a slightly different version of the two-state protocol, where they need to assume the perfect knowledge of the probability distribution p(y|x) of Bob's measurements results given Alice's results. The performance of the four-state protocol with a homodyne detection is presented on Figure 6 for an realistic reconciliation efficiency of 80% as well as a realistic quantum efficiency of 60% for Bob's detector (which is treated as part of the overall loss between Alice and Bob).…”

“…In Section 2, we describe CV QKD protocols with a discrete modulation and we insist particularly on two instances of such protocols for which good error correction schemes are known: the four-state protocol first recently introduced in [15] as well as a two-state protocol quite similar to the protocol considered in [22]. Then, in Section 3, we present the general outline of the security proofs of such protocols.…”

Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation

“…Among possible approaches, two-state protocols were studied in [17], and the authors proved the security of the protocols against any collective attacks, but with the caveat that a complete tomography of the state was required. In [16,18], the authors considered the noises and correlations measured by Alice and Bob from their nonGaussian modulation, and then considered the Gaussian attacks associated with these values as optimal.…”

High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing

“…A high SKR is enabled by the electrical noise suppression in these systems, but with the price of limited bandwidth and high cost. Given that most of the state-of-art error correction codes are developed for discrete modulation, it is necessary to bridge the gap between CV-QKD and discrete modulation to facilitate the reconciliation efficiency [14][15][16]. CV-QKD protocols based on discrete modulation, e.g., the four-state protocol, have been proved to be secure against collective attacks [17].…”