# Phase error estimation for passive detection setups with imperfections and memory effects

## TL;DR

This paper introduces a comprehensive framework for bounding phase error rates in quantum key distribution with passive detection, accounting for imperfections and memory effects, enhancing security proofs and key rate calculations.

## Contribution

It provides a novel, adaptable framework for phase error estimation that incorporates imperfections and memory effects, improving security analysis and key rate computation in quantum cryptography.

## Key findings

- Framework effectively bounds phase error rates with imperfections.
- Allows higher repetition rates in protocols with memory effects.
- Enables more accurate key rate calculations under realistic conditions.

## Abstract

We develop a generic framework to bound the phase error rate for quantum key distribution protocols using passive detection setups with imperfections and memory effects. This framework can be used in proof techniques based on the entropic uncertainty relation or phase error correction, to prove security in the finite-size regime against coherent attacks. Our framework can incorporate on-the-fly announcements of click/no-click outcomes on Bob's side. In the case of imperfections without memory effects, it can be combined with proofs addressing source imperfections in a modular manner. We apply our framework to compute key rates for the decoy-state BB84 protocol, when the beam splitting ratio, the detection efficiency, and dark counts of the detectors are only known to be within some ranges. We also compute key rates in the presence of memory effects in the detectors. In this case, our results allow for protocols to be run at higher repetition rates, resulting in a significant improvement in the secure key generation rate.

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Source: https://tomesphere.com/paper/2508.21486