Security of Quantum Key Distribution from Attacker's View

TL;DR

This paper critically examines the security measure of trace distance in Quantum Key Distribution, arguing that its common interpretation as failure probability is incorrect and proposing a more accurate attacker guessing probability measure.

Contribution

It derives the average attacker guessing probability in QKD, clarifies the limitations of trace distance as a security measure, and challenges existing interpretations of security guarantees.

Findings

Trace distance does not accurately represent failure probability.

The attacker guessing probability can be explicitly derived.

Indistinguishability advantage interpretation is invalid.

Abstract

In 2005, trace distance between an ideal quantum state to be distributed and an actual quantum state distributed was introduced as a valid security measure of Quantum Key Distribution (QKD) by R. Renner et al., then it has been perceived that the trace can be interpreted as a maximum failure probability of QKD. While such a perspective has been widely accepted, H. P. Yuen and O. Hirota have been warning that such an interpretation is not correct since 2009. The author of this study has been giving questions on the interpretation of the trace distance based on their criticisms since QIT30 in May 2014, and has been proposing Yuen's idea to evaluate the security of QKD by the probability for the attacker to guess the correct key. However, the author could not give the guessing probability concretely. In this study, the author explains how to derive the average guessing probability for the attacker, where its result equals to Yuen's derivation firstly seen in 2010. From this result, one will see the problems with the maximum failure probability interpretation of the trace distance clearly. This study also explains the indistinguishability advantage interpretation is also invalid.