Uploaded February 2019 | Updated September 2026, 2 weeks ago
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QGR visitor and friend Michel Planat (Senior Research Scientist, University of Franche-Comte, FEMTO-ST) posits the geometry of cosets in the subgroups of the two-generator free group nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. In previous work, it was established that dessins stabilize point-line geometries whose incidence structure reflects the commutation of (generalized) Pauli operators. Now we find that the nonexistence of a dessin for which the commutator precisely corresponds to the commutator of quantum observables on all lines of the geometry is a signature of quantum contextuality. This occurs first at index : in Mermin's square and at index in Mermin's pentagram, as expected. Commuting sets of -qubit observables with are found to be contextual as well as most generalized polygons. A geometrical contextuality measure is introduced.
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Love our work? Help us continue our research by joining our giving circle. Even just $1/month helps us further our cause: quantumgravityresearch.givingcircles.io
QGR visitor and friend Michel Planat (Senior Research Scientist, University of Franche-Comte, FEMTO-ST) posits the geometry of cosets in the subgroups of the two-generator free group nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. In previous work, it was established that dessins stabilize point-line geometries whose incidence structure reflects the commutation of (generalized) Pauli operators. Now we find that the nonexistence of a dessin for which the commutator precisely corresponds to the commutator of quantum observables on all lines of the geometry is a signature of quantum contextuality. This occurs first at index : in Mermin's square and at index in Mermin's pentagram, as expected. Commuting sets of -qubit observables with are found to be contextual as well as most generalized polygons. A geometrical contextuality measure is introduced.
VISIT THE QGR WEBSITE: quantumgravityresearch.org
GET TO KNOW QGR’s RESEARCH SCIENTISTS: quantumgravityresearch.org/about-quantum
READ OUR RESEARCH PAPERS & PRESENTATIONS: quantumgravityresearch.org/portfolio/all-papers
QGR FACEBOOK: facebook.com/QuantumGravityResearch
QGR TWITTER: twitter.com/emergencetheory?lang=en
QGR INSTAGRAM: instagram.com/quantumgravityresearch
KLEE IRWIN'S WEBSITE: kleeirwin.com
