Properties of Entanglement Monotones for Three-Qubit Pure States

Details Properties of Entanglement Monotones for Three-Qubit Pure States Properties of Entanglement Monotones for Three-Qubit Pure States

2001-06-07

arxiv.org/abs/quant-ph/0106042v2

Physics

Quantum Physics

14 pages, REVTeX

Scientific paper

10.1103/PhysRevA.65.052302

Various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability and behavior under measurement are looked at. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state under local unitary transformations. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in [Phys. Rev. A 60, 910 (1999)]. A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another.

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