Combinatorial Topology Of Multipartite Entangled States

Details Combinatorial Topology Of Multipartite Entangled States Combinatorial Topology Of Multipartite Entangled States

2002-07-10

arxiv.org/abs/quant-ph/0207058v3

Physics

Quantum Physics

14 pages, LaTeX2e. Slightly revised version of the poster resented on the International Conference on Quantum Information, Ovi

Scientific paper

With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular examples of separability polytopes for 3-partite systems are explicitly provided. It turns out that this characterisation of entanglement is associated with simulation of arbitrary unitary operations by 1- and 2-qubit gates. A topological description of how entanglement changes in course of such simulation is provided.

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