Three qubit entanglement within graphical Z/X-calculus

Details Three qubit entanglement within graphical Z/X-calculus Three qubit entanglement within graphical Z/X-calculus

2011-03-14

arxiv.org/abs/1103.2811v1

EPTCS 52, 2011, pp. 22-33

Computer Science

Logic in Computer Science

In Proceedings HPC 2010, arXiv:1103.2268

Scientific paper

10.4204/EPTCS.52.3

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.

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