Suppression laws for multi-particle interference in Sylvester interferometers

TL;DR

This paper establishes a necessary and sufficient criterion for suppressing certain output states in multi-particle interference within Sylvester interferometers, advancing understanding of quantum interference effects for bosons and fermions.

Contribution

It introduces a new criterion for output suppression in Sylvester interferometers with multiple particles, extending previous Fourier-based results to a broader class of quantum optical devices.

Findings

Identifies conditions for significant output suppression in Sylvester interferometers.

Provides a criterion applicable to both bosonic and fermionic particles.

Potential applications in quantum source validation and boson sampling verification.

Abstract

Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or anti-bunching. In presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al. recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multi-port beam splitters. Here we study the case in which $2^q$ particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with $2^p \geq 2^q$ modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single photon sources and in the validation of boson sampling machines.