Composable security for practical quantum key distribution with two way classical communication

TL;DR

This paper develops a rigorous method to accurately calculate finite-key effects in practical quantum key distribution protocols that use two-way classical communication, improving security analysis.

Contribution

It introduces a novel approach to handle the dependence in bit tagging probabilities in TWCC-based QKD, enabling precise finite-key analysis.

Findings

Chernoff bound application yields correct key rate estimates.

Explicit formulas relate independent virtual bits to real dependent bits.

Failure probability in key rate calculation is slightly affected.

Abstract

We present methods to strictly calculate the finite-key effects in quantum key distribution (QKD) with error rejection through two-way classical communication (TWCC) for the sending-or-not-sending twin-field protocol. Unlike the normal QKD without TWCC, here the probability of tagging or untagging for each two-bit random group is not independent. We rigorously solve this problem by imagining a virtual set of bits where every bit is independent and identical. We show the relationship between the outcome starting from this imagined set containing independent and identical bits and the outcome starting with the real set of non-independent bits. With explicit formulas, we show that simply applying Chernoff bound in the calculation gives correct key rate, but the failure probability changes a little bit.