---
abstract: 'We introduce a symmetrization technique which can be used as an extra step in some continuous-variable quantum key distribution protocols. By randomizing the data in phase space, one can dramatically simplify the security analysis of the protocols, in particular in the case of collective attacks. The main application of this procedure concerns protocols with postselection, for which security was established only against Gaussian attacks until now. Here, we prove that under some experimentally verifiable conditions, Gaussian attacks are optimal among all collective attacks.'
author:
- Anthony Leverrier
title: 'A symmetrization technique for continuous-variable quantum key distribution'
---

Quantum key distribution (QKD) is the art of distilling a secret key among distant parties, Alice and Bob, in an untrusted environment. The remarkable feature of QKD is that it is secure in an information theoretic sense [@SBC08]. QKD protocols come in two flavors depending on the type of quantum measurement they use: either a photon counting measurement for *discrete-variable* protocols or a homodyne detection for *continuous-variable* (CV) QKD. While the security of the former is now rather well understood (with the notable exceptions of the differential phase shift [@IWY02] and coherent one-way [@SBG05] protocols), security of CV protocols has been 