One-way quantum key distribution: Simple upper bound on the secret key rate

Tobias Moroder, Marcos Curty, Norbert Lütkenhaus
2006 Physical Review A. Atomic, Molecular, and Optical Physics  
We present a simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase. This method is based on a necessary precondition for one-way secret key distillation; the legitimate users need to prove that there exists no quantum state having a symmetric extension that is compatible with the available measurements results. The main advantage of the obtained
more » ... pper bound is that it can be formulated as a semidefinite program, which can be efficiently solved. We illustrate our results by analysing two well-known qubit-based QKD protocols: the four-state protocol and the six-state protocol. Recent results by Renner et al., Phys. Rev. A 72, 012332 (2005), also show that the given precondition is only necessary but not sufficient for unidirectional secret key distillation.
doi:10.1103/physreva.74.052301 fatcat:fm2gixg2gjgcphgrk5szrfz2gu