@article {1866,
title = {Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States},
journal = {Quantum Information and Computation},
volume = {11},
year = {2011},
month = {2001/09/01},
pages = {813{\textendash}819},
abstract = {In this brief report, we consider the equivalence between two sets of\ *m*\ + 1 bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree m matrix polynomials are unitarily equivalent; i.e.\ *UAiV*\† =\ *Bi*\ for 0 \≤\ *i*\ \≤\ *m*\ where\ *U*\ and\ *V*\ are unitary and (*Ai, Bi*) are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices\ *U*\ and\ *V*.

},
keywords = {matrix polynomials, Schwartz-Zippel lemma, unitary transformations},
issn = {1533-7146},
url = {http://dl.acm.org/citation.cfm?id=2230936.2230942},
author = {Chitambar, Eric and Carl Miller and Shi, Yaoyun}
}