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Properties of entanglement monotones for three-qubit pure states

Gingrich, R. M. (2002) Properties of entanglement monotones for three-qubit pure states. Physical Review A, 65 (5). Art. No. 052302. ISSN 1050-2947. doi:10.1103/PhysRevA.65.052302.

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Various parametrizations 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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Additional Information:©2002 The American Physical Society. Received 3 July 2001; published 15 April 2002. I would like to thank John Preskill for supporting me during this research and for many helpful discussions. I would also like to thank Todd Brun, Sumit Daftuar, Julia Kempe, Michael Nielsen, Federico Spedalieri, Frank Verstraete, Guifre Vidal, Anthony Sudbery, and David Whitehouse for interesting discussions. I thank S. Daftuar and D. Whitehouse in particular for assistance in proving Theorem 2.
Issue or Number:5
Record Number:CaltechAUTHORS:GINpra02
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5944
Deposited By: Tony Diaz
Deposited On:09 Nov 2006
Last Modified:08 Nov 2021 20:30

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