Quantum mutual information and quantumness vectors for multi-qubit systems

TL;DR

This paper introduces a new set of quantum correlation measures called dissension vectors, based on multivariate mutual information, which can characterize and differentiate quantum and classical correlations in multi-qubit systems, with applications in quantum communication and algorithms.

Contribution

It proposes a novel quantum correlation measure called dissension vectors, generalizing multivariate mutual information, and demonstrates their effectiveness in analyzing multi-qubit states and quantum information tasks.

Findings

Dissension vectors respond to different aspects of quantumness and correlations.

They can distinguish between classical and quantum correlations in multi-qubit states.

Dissension vectors are useful in assessing security and performance in quantum protocols.

Abstract

We introduce a new information theoretic measure of quantum correlations for multiparticle systems. We use a form of multivariate mutual information -- the interaction information and generalize it to multiparticle quantum systems. There are a number of different possible generalizations. We consider two of them. One of them is related to the notion of quantum discord and the other to the concept of quantum dissension. This new measure, called dissension vector, is a set of numbers -- quantumness vector. This can be thought of as a fine-grained measure, as opposed to measures that quantify some average quantum properties of a system. These quantities quantify/characterize the correlations present in multiparticle states. We consider some multiqubit states and find that these quantities are responsive to different aspects of quantumness, and correlations present in a state. We find that different dissension vectors can track the correlations (both classical and quantum), or quantumness only. As physical applications, we find that these vectors might be useful in several information processing tasks. We consider the role of dissension vectors -- (a) in deciding the security of BB84 protocol against an eavesdropper and (b) in determining the possible role of correlations in the performance of Grover search algorithm. Especially, in the Grover search algorithm, we find that dissension vectors can detect the correlations and show the maximum correlations when one expects.