State-independent contextuality with identical particles

TL;DR

This paper demonstrates that quantum state-independent contextuality persists in systems of multiple identical bosonic and most fermionic qudits, challenging previous conjectures about the loss of contextuality due to particle indistinguishability.

Contribution

It proves the existence of state-independent contextuality in systems of identical bosonic qudits and most fermionic qudits, providing explicit methods for generating contextual correlations.

Findings

State-independent contextuality exists for bosonic qudits.

Most fermionic qudits exhibit contextuality, except when d fermionic qudits.

Explicit methods to produce contextual correlations are provided.

Abstract

It has been recently conjectured that the state-independency of quantum contextuality may be lost when the indistinguishability of identical particles is taken into account. Here, we show that quantum state-independent contextuality exists for any system of more than one identical bosonic qudits, and for most systems of fermionic qudits. The only exception is the case of d fermionic qudits, since there the dimension of the antisymmetric subspace is 1, which is insufficient for contextuality. For all the other cases, either the symmetry precludes the existence of physical states, or we provide an explicit method to produce quantum state-independent contextual correlations.