Improving key rates of the unbalanced phase-encoded BB84 protocol using the flag-state squashing model

TL;DR

This paper enhances the security analysis of unbalanced phase-encoded BB84 quantum key distribution by applying the flag-state squashing model, leading to higher key rates without changing the experimental setup.

Contribution

It introduces the use of the flag-state squashing model for unbalanced signals, improving key rate estimates in low-loss regimes compared to previous methods.

Findings

Significantly higher key rates in low-loss regimes.

Improved security analysis using the flag-state squashing model.

Key rate gains when part of the loss is trusted or known.

Abstract

All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice. Thus, the original security analyses a priori do not apply to them. Previous security proofs use signal tagging of multi-photon pulses to recover the behaviour of regular BB84. This is overly conservative, as for unbalanced signals, the photon-number splitting attack does not leak full information to Eve. In this work, we exploit the flag-state squashing model to preserve some parts of the multi-photon generated private information in our analysis. Using a numerical proof technique, we obtain significantly higher key rates compared with previously published results in the low-loss regime. It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regime. Thus, we discuss the trusted dark count scenario in this paper as well. We also report a gain in key rates when part of the total loss is known to be induced by a trusted device. We highlight that all these key rate improvements can be achieved without modification of the experimental setup.