Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space

Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a singleparty asymptotic version of this quantum de Finetti theorem in phase space is derived. 5 Author to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 115009 1367-2630/09/115009+12$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft