Generalized interference of fermions and bosons

Abstract

Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of particles. In an experiment with $n$ particles the expressions we derive contain a term for each partition of the integer $n$; Gamas's theorem is used to determine which of these terms are automatically zero based on the pairwise level of distinguishability between particles. Most sampling schemes (such as ``boson sampling'') are limited to completely indistinguishable particles; our paper aids in the understanding of systems where an arbitrary level of distinguishability is permitted. As an application of our paper we introduce a sampling scheme with partially-distinguishable fermions, which we call ``generalized fermion sampling''.