| Tripartite entanglement transformations and tensor rank. | |
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MedLine Citation:
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PMID: 18851511 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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A basic question regarding quantum entangled states is whether one can be probabilistically converted to another through local operations and classical communication exclusively. While the answer for bipartite systems is known, we show that for tripartite systems, this question encodes some of the most challenging open problems in mathematics and computer science. In particular, we show that there is no easy general criterion to determine the feasibility, and in fact, the problem is NP hard. In addition, we find obtaining the most efficient algorithm for matrix multiplication to be precisely equivalent to determining the maximum rate to convert the Greenberger-Horne-Zeilinger state to a triangular distribution of three EPR states. Our results are based on connections between multipartite entanglement and tensor rank (also called Schmidt rank), a key concept in algebraic complexity theory. |
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Authors:
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Eric Chitambar; Runyao Duan; Yaoyun Shi |
Publication Detail:
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Type: Journal Article Date: 2008-10-02 |
Journal Detail:
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Title: Physical review letters Volume: 101 ISSN: 0031-9007 ISO Abbreviation: Phys. Rev. Lett. Publication Date: 2008 Oct |
Date Detail:
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Created Date: 2008-10-14 Completed Date: 2008-11-04 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 0401141 Medline TA: Phys Rev Lett Country: United States |
Other Details:
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Languages: eng Pagination: 140502 Citation Subset: - |
Affiliation:
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Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA. echitamb@umich.edu |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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