Multiparty Quantum Mutual Information: An alternative definition

TL;DR

This paper introduces an alternative, non-negative definition of multipartite quantum mutual information that accounts for shared information among multiple parties, and explores its implications for quantum discord and correlations.

Contribution

It proposes a new multipartite quantum mutual information measure that maintains key properties and extends the concept of quantum discord to multiple parties.

Findings

Quantum discord increases with measurements on more subsystems.

Symmetric quantum discord reveals maximal quantumness among parties.

The new measure aligns with existing measures for pure states.

Abstract

Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two subsystems. This may, however, no longer be true for three or more party quantum systems. In this paper, we propose an alternative definition of multipartite information taking into account the shared information between two and more parties. It is non-negative, observes monotonicity under partial trace as well as completely positive maps, and equals multipartite information measure in literature for pure states. We then define multiparty quantum discord, and give some examples. Interestingly, we observe that quantum discord increases when measurement is performed on a large number of subsystems. Consequently, the symmetric quantum discord, which involves measurement on all parties, reveals the maximal quantumness. This raises question on the interpretation of measured mutual information as classical correlation.