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

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 Rényi 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.

10 pages, one figure. The paper is published in Quantum Information Processing, Howard Brandt memorial issue

References in corpus (5)

• Rényi entropy uncertainty relation for successive projective measurements
• On generalized entropies and information-theoretic Bell inequalities under decoherence
• On the Brukner-Zeilinger approach to information in quantum measurements
• The world according to Renyi: Thermodynamics of multifractal systems
• On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

Cited by in corpus (3)

• Coherence quantifiers from the viewpoint of their decreases in the measurement process
• Individual attacks with generalized discrimination and inadequacy of some information measures
• Cryptographic Security Concerns on Timestamp Sharing via Public Channel in Quantum Key Distribution Systems