  Proving the unconditional security of a quantum key distribution (QKD) scheme
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 very natural way to address this problem is to make an
extensive use of the symmetries of the protocols. In this article, we
investigate a 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.
