Abstract
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.
Highlights
The quantum de Finetti theorem is quite powerful as it allows us to derive the security of a quantum key distribution (QKD) scheme against arbitrary attacks as soon as it is proven
The impossibility of a general dimension-independent theorem does not rule out the possibility of more restricted versions of the theorem, which may still be highly relevant to prove the security of QKD schemes
The phase space representation is the natural choice for the analysis of continuous-variable QKD, where the information is typically encoded onto the quadratures of the light field
Summary
The goal of this section is to explain how symmetry considerations can simplify the theoretical analysis of quantum cryptography. Let us, for instance, consider symmetry under permutations of the subsystems of ρAB which is the symmetry commonly used in various QKD security proofs (with the notable exception of protocols such as the differential phase shift (DPS) [16] or the coherent one-way (COW) [17]). This symmetry can be enforced in the following way: Alice and Bob can perform the same random permutation π over their respective state, with π being chosen uniformly over the symmetric group Sn. This symmetry can be enforced in the following way: Alice and Bob can perform the same random permutation π over their respective state, with π being chosen uniformly over the symmetric group Sn This is what we will do for continuous-variable protocols
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
