Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities

TL;DR

This paper demonstrates that quantum contextuality can be shown for indistinguishable particles, including fermions and bosons, using simple projective measurements, revealing a fundamental link between complementarity and contextuality.

Contribution

It provides a systematic method to demonstrate quantum contextuality for indistinguishable particles of any Hilbert space dimension using only projective measurements.

Findings

Quantum contextuality can be demonstrated for indistinguishable particles.

Applicable to single fermions, multiple fermions, and composite bosons.

Connects complementarity with quantum contextuality.

Abstract

Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While various proofs of such contextual behavior of quantum systems have been established, relatively little is known concerning the possibility to demonstrate this intriguing feature for indistinguishable particles. Here, we show in a simple and systematic manner that with projective measurements alone, it is possible to demonstrate quantum contextuality for such systems of arbitrary Hilbert space dimensions, including those corresponding to a qubit. Our demonstration is applicable to a single fermion as well as multiple fermions, and thus also a composite boson formed from an even number of fermions. In addition, our approach gives a clear demonstration of the intimate connection between complementarity and contextuality, two seemingly unrelated aspects of quantum theory.