A variant of Peres-Mermin proof for testing noncontextual realist models

TL;DR

This paper introduces a new symmetric set of observables for a two-qubit system that provides a state-independent contradiction of quantum mechanics with noncontextual realist models, extending the Peres-Mermin proof.

Contribution

It presents a novel symmetric observable set and an associated inequality for testing noncontextual realism, enhancing previous proofs with a new, experimentally testable approach.

Findings

Quantum violation confirmed for all states in four-dimensional systems.

New symmetric observables lead to a state-independent contradiction.

Proposed inequality can be empirically tested in experiments.

Abstract

For any state in 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 system was used. We, in this letter, 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.