Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications
arXiv:2305.08267 · doi:10.1103/PhysRevA.110.012205
Abstract
Recently, handling of contextual sets, in particular Kochen-Specker (KS) sets, in higher dimensions has been given an increasing attention, both theoretically and experimentally. However, methods of their generation are diverse, not generally applicable in every dimension, and of exponential complexity. Therefore, we design a dimensional upscaling method, whose complexity does not scale with dimension. As a proof of principle we generate manageable-sized KS master sets in up to 27 dimensional spaces and show that well over 32 dimensions can be reached. From these master sets we obtain an ample number of smaller KS sets. We discuss three kinds of applications that work with KS sets in higher dimensions. We anticipate other applications of KS sets for quantum information processing that make use of large families of nonisomorphic KS sets.
arXiv comment17 pages, 13 figures, 1 table, 14 appendices, minor corrections
References in corpus (44)
- Contextuality supplies the magic for quantum computation
- Qudits and high-dimensional quantum computing
- Quantum Cryptography using larger alphabets
- State-independent experimental test of quantum contextuality
- Multi-photon entanglement in high dimensions
- Bell-Kochen-Specker theorem: A proof with 18 vectors
- Generation and Confirmation of a (100x100)-dimensional entangled Quantum System
- Device-independent tests of classical and quantum dimensions
- Experimental test of quantum contextuality in neutron interferometry
- Automated Search for new Quantum Experiments
- High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments
- State-independent quantum contextuality with single photons
- Kochen-Specker Contextuality
- Testing contextuality on quantum ensembles with one clean qubit
- Realization of All-or-nothing-type Kochen-Specker Experiment with Single Photons
- A lower bound on the dimension of a quantum system given measured data
- Experimental implementation of a Kochen-Specker set of quantum tests
- Applying the simplest Kochen-Specker set for quantum information processing
- Kochen-Specker Vectors
- State independent contextuality advances one-way communication
- A scheme for universal high-dimensional quantum computation with linear optics
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality
- Kochen-Specker set with seven contexts
- Converting contextuality into nonlocality
- Contextuality as a resource for measurement-based quantum computation beyond qubits
- Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem
- Realization of a quantum random generator certified with the Kochen-Specker theorem
- Recursive proof of the Bell-Kochen-Specker theorem in any dimension
- New Kochen-Specker Sets in Four Dimensions
- Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
- Gadget structures in proofs of the Kochen-Specker theorem
- Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
- 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
- Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry
- The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
- Automated generation of Kochen-Specker sets
- Hypergraph Contextuality
- Experimental test of high-dimensional quantum contextuality based on contextuality concentration
- Kochen-Specker sets and Hadamard matrices
- The Golay codes and Quantum Contextuality
- Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces
- Vector Generation of Contextual Sets