Normal forms and entanglement measures for multipartite quantum states

Details Normal forms and entanglement measures for multipartite quantum states Normal forms and entanglement measures for multipartite quantum states

2001-05-18

arxiv.org/abs/quant-ph/0105090v5

Phys. Rev. A 68, 012103 (2003)

Physics

Quantum Physics

Proof of uniqueness of normal form added

Scientific paper

10.1103/PhysRevA.68.012103

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence and the 3-tangle), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover a natural extension of the definition of GHZ-states to e.g. $2\times 2\times N$ systems is obtained.

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