Contextuality of identical particles

There exist quantum phenomena that cannot be explained by noncontextual hidden-variable theories, yet the majority of them requires measurements that are performed on a single quantum system at a time. This fact constrains the phenomenon of contextuality to the microscopic domain. It is therefore natural to ask if quantum contextuality can be observed in measurements on collections of particles. Since particles in nature are identical, one can expect that such contextuality would be linked to bosonic and fermionic properties. Analysis of quantum contextuality in such scenarios would broaden our understanding of nonclassical effects in composite systems and perhaps would give us a hint on how to observe quantum phenomena in the macroscopic world. In this work I propose a generalization of quantum contextuality to the case of many identical particles. I show that a type of contextuality exhibited by a collection of particles (state dependent, state independent, or noncontextual) depends on their type and their number. I also discuss further properties of this generalization and identify major open questions.

Figure 1

A hypergraph from Ref. [16] representing measurements in the 18-projector KS scenario in dimension $d=4$ [15]. Hyperedges (grey and orange rectangular areas) correspond to measurement contexts, i.e., sets of mutually orthogonal projectors (modes). The projectors in the right-hand column are unnormalized.

Figure 2

Possible mode assignments of two fermions in the 18-projector KS set. Solid nodes correspond to particles and empty nodes correspond to holes. These assignments exhibit a symmetry between particles and holes; i.e., if one exchanges particles with holes one obtains the same assignment (up to the reflection denoted by the dashed lines).

Figure 3

Mode assignments and contradictions in the Hardy-like proofs of contextuality for two identical particles. The contexts with contradictory assignments are denoted by dashed hyperedges.