Characterizing four-body indistinguishability via symmetries

TL;DR

This paper develops a method to characterize the indistinguishability of up to four identical particles using symmetry-based counting statistics, enabling insights into their internal states and collective phases.

Contribution

It introduces a novel approach to analyze multi-particle indistinguishability through symmetry and counting statistics, extending to mixed internal states and phase information.

Findings

Method for characterizing four-particle indistinguishability

Ability to reconstruct many-particle density operators

Insights into internal degrees of freedom and phases

Abstract

We show how to characterize the indistinguishability of up to four identical, bosonic or fermionic particles, which are rendered partially distinguishable through their internal degrees of freedom prepared in mixed states. This is accomplished via their counting statistics when subjected to a highly symmetric unitary acting upon their external (i.e., dynamical) degrees of freedom. For pure internal states, we further extract information on the particles' collective phases, which ultimately allows for an experimental reconstruction of the full many-particle density operator up to complex conjugation.