Three qubit entanglement within graphical Z/X-calculus

Bob Coecke
(Oxford University Computing Laboratory)
Bill Edwards
(Oxford University Computing Laboratory)

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.

Invited Presentation in Farid Ablayev, Bob Coecke and Alexander Vasiliev: Proceedings CSR 2010 Workshop on High Productivity Computations (HPC 2010), Kazan, Russia, June 21-22, 2010, Electronic Proceedings in Theoretical Computer Science 52, pp. 22–33.
Published: 9th March 2011.

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