Tripartite entanglement transformations and tensor rank

Eric Chitambar, Runyao Duan, Yaoyun Shi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number140502
JournalPhysical review letters
Issue number14
StatePublished - Oct 2 2008
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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