Discriminating distinguishability

TL;DR

This paper introduces a representation theoretic approach to particle distinguishability in quantum photonics, framing it as a state discrimination problem and deriving bounds for complex interferometric setups.

Contribution

It develops a first quantisation formalism to analyze distinguishability, generalizes HOM experiments to multi-particle scenarios, and provides analytical and numerical bounds on discrimination success.

Findings

HOM effect is a special case of state discrimination.

Quantum Fourier Transform is suboptimal for full distinguishability.

Derived bounds for multi-particle, multi-mode discrimination success.

Abstract

Particle distinguishability is a significant challenge for quantum technologies, in particular photonics where the Hong-Ou-Mandel (HOM) effect clearly demonstrates it is detrimental to quantum interference. We take a representation theoretic approach in first quantisation, separating particles' Hilbert spaces into degrees of freedom that we control and those we do not, yielding a quantum information inspired bipartite model where distinguishability can arise as correlation with an environment carried by the particles themselves. This makes clear that the HOM experiment is an instance of a (mixed) state discrimination protocol, which can be generalised to interferometers that discriminate unambiguously between ideal indistinguishable states and interesting distinguishable states, leading to bounds on the success probability of an arbitrary HOM generalisation for multiple particles and modes. After setting out the first quantised formalism in detail, we consider several scenarios and provide a combination of analytical and numerical results for up to nine photons in nine modes. Although the Quantum Fourier Transform features prominently, we see that it is suboptimal for discriminating completely distinguishable states.