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

Anthony Leverrier (1) , E. Karpov (2) , Philippe Grangier (3) , Nicolas Cerf (2, 4)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Ecole Polytechnique de Bruxelles
3 Laboratoire Charles Fabry de l'Institut d'Optique / Optique quantique
4 MIT - Massachusetts Institute of Technology

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 single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.

Domains: Quantum Physics [quant-ph]

Anthony Leverrier, E. Karpov, Philippe Grangier, Nicolas Cerf. Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space. New Journal of Physics, 2009, 11, pp.115009. ⟨10.1088/1367-2630/11/11/115009⟩. ⟨hal-00554926⟩