Continuous-variable quantum cryptography with discrete alphabets: Composable security under collective Gaussian attacks

TL;DR

This paper analyzes the security of continuous-variable quantum key distribution protocols with discrete alphabets, providing a composable security proof under collective Gaussian attacks and finite-size effects.

Contribution

It offers the first composable security analysis for such protocols under realistic assumptions, including finite-size effects and collective Gaussian attacks.

Findings

Efficient parameter estimation via maximum likelihood methods.

Security bounds established under collective Gaussian attack assumptions.

Applicability to protocols using displaced Gaussian states.

Abstract

We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states. In this setting, we provide a composable security analysis in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks. Under this assumption, we can efficiently estimate the parameters of the channel via maximum likelihood estimators and bound the corresponding error in the final secret key rate.