Construction of State-independent Proofs for Quantum Contextuality

TL;DR

This paper introduces a systematic method to construct state-independent proofs of quantum contextuality using Gram matrices, simplifying experimental setups and extendable to higher-dimensional quantum systems.

Contribution

It presents a novel, programmable approach to generate state-independent proofs from sets of rays, enhancing experimental feasibility and generalizability to higher dimensions.

Findings

Constructed proofs from Gram matrices of rays in $\\mathbb{C}^3$

Method simplifies experimental arrangements for quantum contextuality tests

Proofs can be generalized to higher-dimensional systems

Abstract

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the non-contextual hidden variable theory of our nature at the microscopic scale. The conflict between the non-contextual hidden variable theory and quantum mechanics is commonly revealed by Kochen-Specker (KS) sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we first propose a systematic and programmable construction of a state-independent proof from a given set of nonspecific rays in $\mC^3$ according to their Gram matrix. This approach brings us a greater convenience in the experimental arrangements. Besides, our proofs in $\mC^3$ can also be generalized to any higher dimensional systems by a recursive method.