Security of quantum key distribution with detection-efficiency mismatch in the single-photon case: Tight bounds

TL;DR

This paper improves the bounds on the secret key rate in quantum key distribution with detection-efficiency mismatch, providing tight bounds under single-photon assumptions and introducing new analytical methods and adaptations of the decoy state technique.

Contribution

It offers the first tight bounds for secret key rate with constant detection-efficiency mismatch in single-photon QKD and introduces a new analytical minimization method for quantum coherence.

Findings

Derived tight bounds for secret key rate under efficiency mismatch.

Proposed a new analytical method based on relative entropy of coherence.

Adapted the decoy state method for security proof with weak coherent pulses.

Abstract

One of the challenges in practical quantum key distribution is dealing with efficiency mismatch between different threshold single-photon detectors. There are known bounds for the secret key rate for the BB84 protocol with detection-efficiency mismatch provided that the eavesdropper sends no more than one photon to the legitimate receiver. Here we improve these bounds and give tight bounds for the secret key rate with a constant detection-efficiency mismatch under the same single-photon assumption. We propose a method based on the analytical minimization of the relative entropy of coherence, which can be used in other problems in quantum key distribution. Also we propose an adaptation of the decoy state method to proof the security in the case of weak coherent pulses on the source side.