A central limit theorem for partially distinguishable bosons

TL;DR

This paper extends the quantum central limit theorem to partially distinguishable bosons, revealing how internal degrees of freedom influence equilibration and providing diagnostic tools for experimental imperfections.

Contribution

It generalizes the Cushen-Hudson quantum central limit theorem to include partial distinguishability effects in bosonic systems.

Findings

Subsystem states converge to multimode Gaussian states

Particle number distributions reveal distinguishability signatures

Implications for large boson sampling experiments

Abstract

The quantum central limit theorem derived by Cushen and Hudson provides the foundations for understanding how subsystems of large bosonic systems evolving unitarily do reach equilibrium. It finds important applications in the context of quantum interferometry, for example, with photons. A practical feature of current photonic experiments, however, is that photons carry their own internal degrees of freedom pertaining to, e.g., the polarization or spatiotemporal mode they occupy, which makes them partially distinguishable. The ensuing deviation from ideal indistinguishability is well known to have observable consequences, for example in relation with boson bunching, but an understanding of its role in bosonic equilibration phenomena is still missing. Here, we generalize the Cushen-Hudson quantum central limit theorem to encompass scenarios with partial distinguishability, implying an asymptotic convergence of the subsystem's reduced state towards a multimode Gaussian state defined over the internal degrees of freedom. While these asymptotic internal states may not be directly accessible, we show that particle number distributions carry important signatures of distinguishability, which may be used to diagnose experimental imperfections in large boson sampling experiments.