Symmetric extension and its application in QKD

Abstract

We investigate the distillation of secret key from classical data when these data are derived from quantum states by measurements. Underlying quantum states with a so‐called symmetric extension can never lead to a secret key via one‐way communication but must be processed further by LOCC operations. We show that if a symmetric extension can be broken by LOCC operations, it is also possible to break it with a single filter. For Bell‐diagonal and some other two‐qubit states we characterize the states with symmetric extension, and give a conjectured formula for the general two‐qubit case. We apply these results to the the 4‐state and 6‐state QKD protocols to show that the two‐way procedure proposed by Chau fails for error rates beyond 20% and 27.6% precisely because at that point it fails to break symmetric extensions.