Quantum Mutual Information Along Unitary Orbits

TL;DR

This paper investigates how quantum mutual information varies along unitary orbits of bipartite states, providing solutions for two-qubit systems, exploring effects of unitary operations, and analyzing correlation optimization in higher dimensions.

Contribution

It offers a full optimization solution for two-qubit systems and characterizes states with minimal correlations, including a novel 'Young tableau' structure for separable states.

Findings

Maximization of correlations is straightforward for equal-sized subsystems.

Minimal correlations exhibit complex structures and are characterized by 'Young tableau' states.

A partial order based on marginal entropies influences the correlation optimization process.

Abstract

Motivated by thermodynamic considerations, we analyse the variation of the quantum mutual information on a unitary orbit of a bipartite system's state, with and without global constraints such as energy conservation. We solve the full optimisation problem for the smallest system of two qubits, and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems, such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward for equal-sized subsystems, however their minimisation displays non-trivial structures. We characterise a set of separable states in which the minimally correlated state resides: a collection of classically correlated states admitting a particular "Young tableau" form. Furthermore, a partial order exists on this set with respect to individual marginal entropies, and the presence of a "see-saw effect" for these entropies forces a finer analysis to determine the optimal tableau.