State-independent proof of Kochen-Specker theorem with 13 rays
arXiv:1109.4396 · doi:10.1103/PhysRevLett.108.030402
Abstract
Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems. However for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state-dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all non-contextual realistic models while being violated by all qutrit states. Thus our inequality will practically facilitate a state-independent test of the quantum contextuality for an indivisible quantum system. We provide also a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a three by three magic cube.
5 pages, 2 figures
References in corpus (8)
- 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
- Experimental test of quantum contextuality in neutron interferometry
- State-independent quantum contextuality with single photons
- Universality of state-independent violation of correlation inequalities for noncontextual theories
- Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes
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