Vector Generation of Contextual Sets
arXiv:1905.01784 · doi:10.1051/epjconf/201919800009
Abstract
As quantum contextuality proves to be a necessary resource for universal quantum computation, we present a general method for vector generation of Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method supersedes all three previous methods: (i) fortuitous discoveries of smallest KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random downward generation of sets from fortuitously obtained big master sets. In contrast to previous works, we can generate master sets which contain all possible KS sets starting with nothing but a few simple vector components. From them we can readily generate all KS sets obtained in the last half a century and any specified new KS sets. Herewith we can generate sufficiently large sets as well as sets with definite required features and structures to enable varieties of different implementations in quantum computation and communication.
6 pages, 6 figures; Orally presented by M. Pavicic at Quantum Technology International Conference 2018 (QTech 2018), Paris, France, September 5-7, 2018; Extended version: https://www.youtube.com/watch?v=Bw2vItz5trE
References in corpus (37)
- Contextuality supplies the magic for quantum computation
- State-independent experimental test of quantum contextuality
- Bell-Kochen-Specker theorem: A proof with 18 vectors
- Experimental test of quantum contextuality in neutron interferometry
- 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
- A feasible "Kochen-Specker" experiment with single particles
- Experiments towards Falsification of Noncontextual Hidden Variable Theories
- Proposed experimental tests of the Bell-Kochen-Specker theorem
- Kochen-Specker theorem for 8-dimensional space
- Proposed experiment for testing quantum contextuality with neutrons
- Applying the simplest Kochen-Specker set for quantum information processing
- Kochen-Specker Vectors
- Proposal for revealing quantum nonlocality via local contextuality
- Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality
- Kochen-Specker set with seven contexts
- Proofs of the Kochen-Specker theorem based on a system of three qubits
- Entanglement in eight-qubit graph states
- Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem
- Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
- On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits
- New Kochen-Specker Sets in Four Dimensions
- Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
- Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions
- Kochen-Specker theorem as a precondition for secure quantum key distribution
- Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
- Graph Approach to Quantum Systems
- Probabilistic Generation of Quantum Contextual Sets
- Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
- Parity proofs of the Kochen-Specker theorem based on the 120-cell
- Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem
- Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry
- New Class of 4-Dim Kochen-Specker Sets
- The Penrose dodecahedron and the Witting polytope are identical in CP(3)
- The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
- Kochen-Specker Sets and Generalized Orthoarguesian Equations