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arXiv · 1911.11401

A Finite-Geometric Classification of Three-Qubit Mermin Pentagrams

Metod Saniga·Frederic Holweck·Hamza Jaffali
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Abstract

Given the facts that the three-qubit symplectic polar space features three different kinds of observables and each of its labeled Fano planes acquires a definite sign, we found that there are 45 distinct types of Mermin pentagrams in this space. A key element of our classification is the fact that any context of such pentagram is associated with a unique (positive or negative) Fano plane. Several intriguing relations between the character of pentagrams' three-qubit observables and `valuedness' of associated Fano planes are pointed out. In particular, we find two distinct kinds of negative contexts and as many as four positive ones.

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Metod Saniga, Frederic Holweck, Hamza Jaffali. 2019-11-26. A Finite-Geometric Classification of Three-Qubit Mermin Pentagrams. https://doi.org/10.3390/sym12040534

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