Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Topological Quantum Computing Quantum Simulation Quantum State Preparation Representation Entanglement Theory Quantum Correlations

Geometric contextuality from the Maclachlan-Martin Kleinian groups

arXiv
Authors: Michel Planat

Year

2015

Paper ID

27354

Status

Preprint

Abstract Read

~2 min

Abstract Words

132

Citations

N/A

Abstract

There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry mathcal{G} of a subgroup H of the two-generator free group G=leftlangle x,yrightrangle. One defines geometric contextuality from the discrepancy between the commutativity of cosets on mathcal{G} and that of quantum observables.It is shown in this paper that Kleinian subgroups K=leftlangle f,grightrangle that are non-compact, arithmetic, and generated by two elliptic isometries f and g (the Martin-Maclachlan classification), are appropriate contextuality filters. Standard contextual geometries such as some thin generalized polygons starting with Mermin's $3 times 3$ grid belong to this frame. The Bianchi groups PSL\(2,O\d\), d in \{1,3\} defined over the imaginary quadratic field O\d=mathbb{Q}\(sqrt{-d}\) play a special role.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2015 reference point for readers tracking recent quantum research.
  • There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry mathcalG of a subgroup H of the two-generator free group...

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.02466 [2] arXiv https://arxiv.org/abs/1509.02466 [3] Publisher https://arxiv.org/abs/1509.02466

Local Citation Graph (Related-Paper Links)

Current Paper #27354 #78846 Analog quantum simulation of Sh... #78810 Secure Quantum Handshakes: Quan... #78802 Quantum Co-Design of Inhomogene... #78801 Constructing Large and Structur...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.