Two proposals for testing quantum contextuality of continuous-variable states

TL;DR

This paper proposes two methods to test quantum contextuality in continuous-variable states, demonstrating violations of Kochen-Specker inequalities for various entangled and mixed states using effective observables.

Contribution

It generalizes Kochen-Specker inequality testing to continuous-variable states with new measurement approaches and demonstrates state-independent violations.

Findings

Violation of KS inequalities shown for entangled coherent states.

Effective bidimensional observables enable testing of contextuality.

Theoretical proof of KS inequality violation for any two-mode state.

Abstract

We investigate the violation of non-contextuality by a class of continuous variable states, including variations of entangled coherent states (ECS's) and a two-mode continuous superposition of coherent states. We generalise the Kochen-Specker (KS) inequality discussed in A. Cabello, Phys. Rev. Lett. {\bf 101}, 210401 (2008) by using effective bidimensional observables implemented through physical operations acting on continuous variable states, in a way similar to an approach to the falsification of Bell-CHSH inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudo-spin observables and a generalized quasi-probability function.