OpenAlex ·
Automated search for highly contextual Kochen-Specker proofs
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.19862
- Original
- Read it at the publisher
- Topics
Abstract
Observable-based Kochen-Specker proofs are configurations of multi-qubit Pauli observables grouped into contexts whose products are plus or minus the indentity. Their robustness as state-independent contextuality tests can be measured by the tolerated error per context $\varepsilon = 2d/|H|$, where $d$ is the contextuality degree and $|H|$ the number of contexts. Since the degree depends only on an underlying abstract structure called the hypergram i.e. the pair formed by the context hypergraph and the anticommutation graph, the search for highly contextual proofs can be carried out on them instead, with no reference to qubits or to any particular Pauli labeling. We further exploit this by enumerating anticommutation graphs first, and then by associating to each graph $G$ the single hypergram carrying its entire hypergraph support $HS(G)$, so that exactly one candidate is examined per graph. Applied to the House of Graphs database and to censuses of vertex-transitive graphs on at most 24 vertices, this pipeline recovers the Peres-Mermin square, the doily and the Mermin pentagram, and yields configurations reaching $\varepsilon = 0.707$, against $0.424$ for the previous published record. The best configurations are predominantly those stemming from line graphs and unions of graphs; we explain the former by showing that every perfect matching of a graph is a context of its line graph, which exhibits the Peres-Mermin square and the doily as the first members of two infinite families. We close with finite geometric descriptions of the most striking configurations inside symplectic polar spaces, in terms of ovoids, hyperbolic quadrics and Fano planes.
The authors’ abstract, as arXiv lists it. arXiv’s listings, abstracts included, are free for anyone to reuse.
Read it on ReadSearch
Each opens after you create an account, and brings you back to this paper.
More in Statistical Mechanics
The Mirror Theorem: Central Incidence Saturation in Keith Recurrences
Schwinger stability of T-duality-inspired extremal black holes
Coherence in Biological Systems
Nonlinear dynamics of random neural networks with second-order synaptic motifs
Analytic non-axisymmetric 3D MHD equilibria without stellarator symmetry
Get the few papers worth your time in Statistical Mechanics every morning.
ReadSearch reads the new papers in your field each day and brings you the few worth reading, each with its key finding in a sentence.