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arXiv:1211.2518 · Physical Review A

Quantum violation of entropic noncontextual inequality in four dimensions

A. K. Pan, M. Sumanth, Prasanta Kumar Panigrahi

Published Jan 18, 2013• 7 citations
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Abstract

Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in a noncontextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of entangled, as well as product states. Our inequality can be experimentally tested using the existing technology.

DOI
10.1103/physreva.87.014104

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Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in a noncontextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of entangled, as well as product states. Our inequality can be experimentally tested using the existing technology.
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves [Phys. Rev. Lett. 61, 662 (1988)], that must be satisfied by all noncontextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.
For any state in a four-dimensional system, the quantum violation of an inequality based on the Peres-Mermin proof for testing noncontextual realist models has experimentally been corroborated. In the Peres-Mermin proof, an array of nine holistic observables for two two-qubit systems was used. In this letter, we present a new symmetric set of observables for the same system which also provides a contradiction of quantum mechanics with noncontextual realist models in a state-independent way. The whole argument can also be cast in the form of a new inequality that can be empirically tested.
We report a state-independent experimental test of quantum contextuality of a single-photon qutrit. The experimental results demonstrate violations of an inequality originally formulated by Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] and further optimized by Cabello et al. [Phys. Rev. A 85, 032108 (2012)]; this inequality is satisfied by all noncontextual hidden variable models and is violated by all qutrit states. Our experiment shows quantum contextuality of this nature in a most fundamental way: A way that is independent of state and unrelated to entanglement.