Taxonomy of Three-Qubit Mermin Pentagrams

Abstract

Given the fact 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.

Keywords

• Mermin pentagrams
• three-qubit symplectic polar space
• valued Fano planes