Phase error rate estimation in QKD with imperfect detectors

TL;DR

This paper provides a finite-size security proof for the decoy-state BB84 quantum key distribution protocol with imperfect detectors, addressing basis-efficiency mismatch and detector side channels using entropic uncertainty relations.

Contribution

It introduces a security proof that handles imperfect detectors and basis-efficiency mismatch without modifying the protocol, applicable to variable-length keys and adversarial detector parameters.

Findings

Security proof applicable to imperfect detectors with characterized efficiency mismatch

Addresses detector side channels by allowing Eve to choose detector parameters within bounds

Demonstrates the impact of basis-efficiency mismatch on protocol security

Abstract

We present a finite-size security proof of the decoy-state BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, for imperfect detectors. We apply this result to the case of detectors with imperfectly characterized basis-efficiency mismatch. Our proof works by obtaining a suitable bound on the phase error rate, without requiring any new modifications to the protocol steps or hardware. It is applicable to imperfectly characterized detectors, and only requires the maximum relative difference in detection efficiencies and dark count rates of the detectors to be characterized. Moreover, our proof allows Eve to choose detector efficiencies and dark count rates in their allowed ranges in each round, thereby addressing an important problem of detector side channels. We prove security in the variable-length framework, where users are allowed to adaptively determine the length of key to be produced, and number of bits to be used for error-correction, based on observations made during the protocol. We quantitatively demonstrate the effect of basis-efficiency mismatch by applying our results to the decoy-state BB84 protocol.