On the spectral dependence of separable and classical correlations in small quantum systems

TL;DR

This paper investigates how spectral properties influence correlations in small quantum systems, revealing unique classical maximum states for mutual information in 2x3 systems and analyzing spectral partial orders.

Contribution

It provides a detailed analysis of spectral dependence of correlations in 2x2 and 2x3 quantum systems, identifying conditions for maximum classical correlations and introducing spectral partial orders.

Findings

Maximal mutual information in 2x2 systems can be fully characterized for certain spectra.

In 2x3 systems, a spectral partial order uniquely determines the classical maximum state.

The 2x3 system is the largest with a spectral partial order that singles out a unique classical maximum.

Abstract

We study the correlation structure of separable and classical states in 2x2- and 2x3-dimensional quantum systems with fixed spectra. Even for such simple systems the maximal correlation - as measured by mutual information - over the set of unitarily accessible separable states is highly non-trivial to compute; however for the 2x2 case a particular class of spectra admits full analysis and allows us to contrast classical states with more general separable states. We analyse a particular entropic partial order on the set of spectra and prove for the qubit-qutrit case that this partial order alone picks out a unique classical maximum state for mutual information. Moreover the 2x3 case is the largest system with such a property.