Three qubit entanglement within graphical Z/X-calculus

TL;DR

This paper uses graphical calculus from categorical quantum mechanics to analyze 3-qubit entanglement, specifically constructing GHZ and W states and introducing a new concept called supplementarity for classifying entanglement.

Contribution

It applies graphical Z/X-calculus to explicitly construct and classify 3-qubit entangled states, extending the methodology to multipartite states with a new supplementarity concept.

Findings

Constructed GHZ and W states within the graphical calculus.

Introduced supplementarity to characterize W-class states.

Extended the approach to general multipartite qubit states.

Abstract

The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the W- and GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstract diagrammatic calculus; these method extends to more general multipartite qubit states.