Tight Finite-Key Analysis for Quantum Cryptography

TL;DR

This paper presents a finite-key security analysis for quantum key distribution protocols, demonstrating that security can be achieved with practical, moderate numbers of signals using a novel proof technique based on smooth entropies.

Contribution

It introduces a finite-key security proof for BB84 protocols using uncertainty relations for smooth entropies, bridging the gap between theory and practical implementation.

Findings

Security guaranteed for moderate signal numbers M

Applicable to general attacks in quantum cryptography

Uses a novel proof technique based on uncertainty relations

Abstract

Despite enormous progress both in theoretical and experimental quantum cryptography, the security of most current implementations of quantum key distribution is still not established rigorously. One of the main problems is that the security of the final key is highly dependent on the number, M, of signals exchanged between the legitimate parties. While, in any practical implementation, M is limited by the available resources, existing security proofs are often only valid asymptotically for unrealistically large values of M. Here, we demonstrate that this gap between theory and practice can be overcome using a recently developed proof technique based on the uncertainty relation for smooth entropies. Specifically, we consider a family of Bennett-Brassard 1984 quantum key distribution protocols and show that security against general attacks can be guaranteed already for moderate values of M.