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

TL;DR

This paper establishes a security bound for finite-resource quantum key distribution protocols with one-way post-processing, demonstrating practical key rates for standard protocols and discussing security for other discrete-variable protocols.

Contribution

It provides a composable security proof for finite-resource QKD protocols under collective attacks, with explicit key rate thresholds for single-qubit implementations.

Findings

Positive secret key rate achievable with ~10^5 signals for standard protocols

Unconditional security can be extended to other protocols via de Finetti theorem but with pessimistic estimates

Security bound is operational and applicable to practical finite-resource scenarios

Abstract

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates.