Testing for multipartite indistinguishability

Abstract

Indistinguishability of subsystems is a requirement for quantum interference, which is in turn the workhorse of extra‐classical demonstrations such as those proposed in quantum information protocols. However, indistinguishability does not arise in the standard axioms of quantum mechanics. Once the standard textbook approach is assumed, the pure states of the system in question are conventionally restricted to a Hilbert subspace with permutation symmetry. From the tomographic perspective, this is unacceptable, as such an assumption of symmetry can be too restrictive. Here we report two approaches to the problem of multiple bosons that admit both distinguishable and indistinguishable states of the same system. In doing so we define two notions of distinguishability. Both approaches are shown to give the same results in the sense that they predict the same restriction on density matrices as would be reconstructed tomographically. The number of unknown elements is polynomial in the number of particles, in stark contrast to the distinguishable case which scales exponentially. We use this picture to investigate possible measurement schemes which could detect and/or characterise indistinguishability.