Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way post-processing

摘要

We derive a bound for the security of QKD with finite resources under one-waypost-processing, based on a definition of security that is composable and hasan operational meaning. While our proof relies on the assumption of collectiveattacks, unconditional security follows immediately for standard protocols likeBennett-Brassard 1984 and six-states. For single-qubit implementations of suchprotocols, we find that the secret key rate becomes positive when at leastN\sim 10^5 signals are exchanged and processed. For any other discrete-variableprotocol, unconditional security can be obtained using the exponential deFinetti theorem, but the additional overhead leads to very pessimisticestimates.