Indistinguishability of identical bosons from a quantum information theory perspective

TL;DR

This paper develops a quantum information theory framework to quantify and analyze the indistinguishability of identical bosons in linear optical experiments, providing operational measures and characterizations of distinguishability states.

Contribution

It introduces a general, assumption-free measure of boson indistinguishability and characterizes states of perfect distinguishability within a quantum information context.

Findings

Operational measure of indistinguishability derived

Tight lower bounds on indistinguishability measure established

Characterization of states with perfect distinguishability provided

Abstract

Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on additional assumptions on the input state of the interferometer, such as, for instance, a fixed mode occupation, nor on any assumption on the degrees of freedom that potentially make the particles distinguishable. We identify the expectation value of the projector onto the $N$-particle symmetric subspace as an operationally meaningful measure of indistinguishability, and derive tight lower bounds on it that can be efficiently measured in experiments. Moreover, we present a consistent definition of perfect distinguishability and characterize the corresponding set of states. In particular, we show that these states are diagonal in the computational basis up to a permutationally invariant unitary. Moreover, we find that convex combinations of states that describe partially distinguishable and perfectly indistinguishable particles can lead to perfect distinguishability, which itself is not preserved under convex combinations.