Construction of State-independent Proofs for Quantum Contextuality
arXiv:1707.05626 · doi:10.1103/PhysRevA.96.062126
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.
arXiv commentA revised viseion with supplemental materials. 10 pages, 6 figures
References in corpus (27)
- Hidden Variables and the Two Theorems of John Bell
- 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
- Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
- Experimental test of quantum contextuality in neutron interferometry
- State-independent proof of Kochen-Specker theorem with 13 rays
- Anomalous Weak Values Are Proofs of Contextuality
- State-independent quantum contextuality with single photons
- Testing contextuality on quantum ensembles with one clean qubit
- Realization of All-or-nothing-type Kochen-Specker Experiment with Single Photons
- Experiments towards Falsification of Noncontextual Hidden Variable Theories
- Universality of state-independent violation of correlation inequalities for noncontextual theories
- State-independent experimental tests of quantum contextuality in a three dimensional system
- Experimental implementation of a Kochen-Specker set of quantum tests
- Kochen-Specker theorem for 8-dimensional space
- A Kochen-Specker inequality
- State-independent experimental test of quantum contextuality in an indivisible system
- A Kochen-Specker inequality from a SIC
- Hidden-variable theorems for real experiments
- Simple Hardy-like proof of quantum contextuality
- Experimental fully contextual correlations
- Necessary and sufficient condition for quantum state-independent contextuality
- Kochen-Specker set with seven contexts
- Greenberger-Horne-Zeilinger paradoxes from qudit graph states
- Recursive proof of the Bell-Kochen-Specker theorem in any dimension