Abstract
The geometry of cosets in the subgroups H of the two-generator free group G =\textless{} a, b \textgreater{} nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. Dessins stabilize point-line incidence geometries that reflect the commutation of (generalized) Pauli operators [Information 5, 209 (2014); 1310.4267 and 1404.6986 (quant-ph)]. Now we find that the non-existence of a dessin for which the commutator (a, b) = a^ (--1) b^( --1) ab precisely corresponds to the commutator of quantum observables [A, B] = AB -- BA on all lines of the geometry is a signature of quantum contextuality. This occurs first at index |G : H| = 9 in Mermin's square and at index 10 in Mermin's pentagram, as expected. Commuting sets of n-qubit observables with n \textgreater{} 3 are found to be contextual as well as most generalized polygons. A geometrical contextuality measure is introduced.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
