Quantum state-independent contextuality requires 13 rays
arXiv:1606.01848 · doi:10.1088/1751-8113/49/38/38LT01
Abstract
We show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three [Phys. Rev. Lett. 108, 030402 (2012)] is actually the minimal set in quantum theory. This contrasts with the case of Kochen-Specker sets, where the smallest set occurs in dimension four.
8 pages, 2 tables, 1 figure, v2: minor changes
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Cited by in corpus (18)
- Kochen-Specker Contextuality
- Sustained state-independent quantum contextual correlations from a single ion
- Converting contextuality into nonlocality
- Optimal classical simulation of state-independent quantum contextuality
- From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
- Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
- Quantum Contextuality
- Graph-theoretic approach to Bell experiments with low detection efficiency
- The magic of universal quantum computing with permutations
- Certifying sets of quantum observables with any full-rank state
- Optimal and tight Bell inequalities for state-independent contextuality sets
- State-independent quantum contextuality with projectors of nonunit rank
- Revealing quantum contextuality using a single measurement device
- The simplest Kochen-Specker set
- Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
- Graph-theoretic approach to dimension witnessing
- Twenty years of quantum contextuality at USTC
- Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive