On conclusive eavesdropping and measures of mutual information in quantum key distribution

TL;DR

This paper investigates how to measure an eavesdropper's information gain in quantum key distribution, comparing different mutual information measures and highlighting issues with Rényi mutual information in conclusive eavesdropping scenarios.

Contribution

It analyzes the effectiveness of conclusive eavesdropping strategies and critiques the validity of Rényi mutual information as a measure in quantum cryptography.

Findings

Helstrom scheme and unambiguous discrimination differ significantly in mutual information quantification.

Rényi mutual information may not be a reliable measure of eavesdropper's information.

Conclusive eavesdropping can be more powerful than traditional methods.

Abstract

We address the question of quantifying eavesdropper's information gain in an individual attack on systems of quantum key distribution. It is connected with the concept of conclusive eavesdropping introduced by Brandt. Using the BB84 protocol, we examine the problem of estimating a performance of conclusive entangling probe. The question of interest depends on the choice of a quantitative measure of eavesdropper's information about the error-free sifted bits. The Fuchs--Peres--Brandt probe realizes a very powerful individual attack on the BB84 scheme. In the usual formulation, Eve utilizes the Helstrom scheme in distinguishing between the two output probe states. In conclusive eavesdropping, the unambiguous discrimination is used. Comparing these two versions allows to demonstrate serious distinctions between widely used quantifiers of mutual information. In particular, the so-called R\'{e}nyi mutual information does not seem to be a completely legitimate measure of an amount of mutual information. It is brightly emphasized with the example of conclusive eavesdropping.