Combinatorial Topology Of Multipartite Entangled States
Abstract
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.
Cite
@article{arxiv.quant-ph/0207058,
title = {Combinatorial Topology Of Multipartite Entangled States},
author = {Roman R. Zapatrin},
journal= {arXiv preprint arXiv:quant-ph/0207058},
year = {2015}
}
Comments
14 pages, LaTeX2e. Slightly revised version of the poster resented on the International Conference on Quantum Information, Oviedo, Spain, 13-18 July, 2002. To appear in the special issue of Journal of Modern Optics