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

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.

9 pages, no figure; Major changes; More changes. Accepted in Scientific Reports

References in corpus (17)

• Hidden Variables and the Two Theorems of John Bell
• Contextuality supplies the magic for quantum computation
• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• Experimental non-classicality of an indivisible quantum system
• State-independent quantum contextuality with single photons
• No extension of quantum theory can have improved predictive power
• Simple explanation of the quantum violation of a fundamental inequality
• Universality of state-independent violation of correlation inequalities for noncontextual theories
• All entangled pure states violate a single Bell's inequality
• State-independent experimental tests of quantum contextuality in a three dimensional system
• The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
• What does an experimental test of quantum contextuality prove or disprove?
• Coexistence of Kochen-Specker inequalities and noncontextuality inequalities
• State-independent contextuality with identical particles
• Is there contextuality for a single qubit?

Cited by in corpus (6)

• Experimental demonstration of quantum contextuality on an NMR qutrit
• A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
• Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
• Contextuality of Identical Particles
• Quantitative relations between different measurement contexts
• Tracing quantum correlations back to collective interferences