Security proof of quantum key distribution with detection efficiency mismatch

TL;DR

This paper proves the unconditional security of quantum key distribution systems despite detection efficiency mismatches, by analyzing their physical origins and proposing a random switching method to mitigate security risks.

Contribution

It provides a comprehensive security proof for QKD with detection efficiency mismatch and introduces a method to eliminate this vulnerability through random detector bit assignment.

Findings

Security can be maintained despite efficiency mismatch

Detection efficiency ratio determines key rate

Random switching of detector assignments eliminates mismatch effects

Abstract

In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.