Hypergraph Contextuality
arXiv:1911.06448 · doi:10.3390/e21111107
Abstract
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets - the Kochen-Specker ones and the operator-based ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities.
15 pages, 6 figures, figures are positioned differently than in the paper - not where they are mentioned first, but where they are discussed the most
References in corpus (15)
- A simple test for hidden variables in spin-1 system
- 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
- Experimental implementation of a Kochen-Specker set of quantum tests
- Proposed experiment for testing quantum contextuality with neutrons
- Applying the simplest Kochen-Specker set for quantum information processing
- Necessary and sufficient condition for quantum state-independent contextuality
- Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
- Graph Approach to Quantum Systems
- Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces
- Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
- Automated generation of Kochen-Specker sets
- New Examples of Kochen-Specker Type Configurations on Three Qubits