`Classical' quantum states

TL;DR

This paper unifies the analysis of various classes of mixed quantum states that are considered 'most classical' in finite-dimensional Hilbert spaces, simplifying their decomposition and characterization.

Contribution

It introduces a unified method to analyze and decompose 'most classical' quantum states, reducing the number of pure states needed for certain decompositions.

Findings

Four pure states suffice for decomposing certain spin-1 states.

Unified approach applies to separable, fermionic, bosonic, and coherent states.

Simplifies understanding of classicality in mixed quantum states.

Abstract

We show that several classes of mixed quantum states in finite-dimensional Hilbert spaces which can be characterized as being, in some respect, 'most classical' can be described and analyzed in a unified way. Among the states we consider are separable states of distinguishable particles, uncorrelated states of indistinguishable fermions and bosons, as well as mixed spin states decomposable into probabilistic mixtures of pure coherent states. The latter were the subject of the recent paper by Giraud et. al., who showed that in the lowest-dimensional, nontrivial case of spin 1, each such state can be decomposed into a mixture of eight pure states. Using our method we prove that in fact four pure states always suffice.