Hexagons govern three-qubit contextuality
arXiv:2312.07738 · doi:10.22331/q-2025-01-20-1601
Abstract
Split Cayley hexagons of order two are distinguished finite geometries living in the three-qubit symplectic polar space in two different forms, called classical and skew. Although neither of the two yields observable-based contextual configurations of their own, {\it classically}-embedded copies are found to fully encode contextuality properties of the most prominent three-qubit contextual configurations in the following sense: for each set of unsatisfiable contexts of such a contextual configuration there exists some classically-embedded hexagon sharing with the configuration exactly this set of contexts and nothing else. We demonstrate this fascinating property first on the configuration comprising all 315 contexts of the space and then on doilies, both types of quadrics as well as on complements of skew-embedded hexagons. In connection with the last-mentioned case and elliptic quadrics we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to substantiate our theoretical findings.
28 pages, 15 figures, published in Quantum
References in corpus (27)
- Hidden Variables and the Two Theorems of John Bell
- Four qubits can be entangled in nine different ways
- Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
- Kochen-Specker Contextuality
- Experimental test of Mermin inequalities on a 5-qubit quantum computer
- Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
- Hjelmslev Geometry of Mutually Unbiased Bases
- Projective Ring Line of an Arbitrary Single Qudit
- Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
- Factor-Group-Generated Polar Spaces and (Multi-)Qudits
- Proposed test of macroscopic quantum contextuality
- Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes
- Experimental Demonstration of Quantum Pseudotelepathy
- The Veldkamp space of multiple qubits
- Distinguished three-qubit 'magicity' via automorphisms of the split Cayley hexagon
- Contextuality with a Small Number of Observables
- The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
- Mermin pentagrams arising from Veldkamp lines for three qubits
- Contextuality degree of quadrics in multi-qubit symplectic polar spaces
- Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
- Primitive Nonclassical Structures of the -qubit Pauli Group
- Experimenting quantum phenomena on NISQ computers using high level quantum programming
- Testing a Bell Inequality with a Remote Quantum Processor
- New and improved bounds on the contextuality degree of multi-qubit configurations
- 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
- Charting the Real Four-Qubit Pauli Group via Ovoids of a Hyperbolic Quadric of PG(7,2)
- Measuring the Mermin-Peres magic square using an online quantum computer