Graph Approach to Quantum Systems
arXiv:1004.0776 · doi:10.1063/1.3491766
Abstract
Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices generated by McKay-Megill-Pavicic (MMP) hypergraphs and Hilbert subspace equations are given. To enable exhaustive generations of 3-dim KS setups by means of recently found "stripping technique," bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks (orthogonal triples of elements) - up to 41 of them. We obtain several new results on such lattices and hypergraphs, in particular on properties such as superposition and orthoraguesian equations. Since a bipartite graph approach has recently been applied to CSS (Calderbank-Shor-Steane) and graph states on the one hand, and span programs, quantum walks, and quantum search on the other, our results also enable the study of these quantum information fields by means of hypergraphs and lattices.
20 pages, 15 figures
References in corpus (4)
Cited by in corpus (13)
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- Quantum Contextuality
- Quantum theory realises all joint measurability graphs
- Probabilistic Generation of Quantum Contextual Sets
- 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
- Hypergraph Contextuality
- New Examples of Kochen-Specker Type Configurations on Three Qubits
- Non-Kochen-Specker Contextuality
- Vector Generation of Contextual Sets
- Chromatic Quantum Contextuality