%0 Journal Article %J Quantum Information and Computation %D 2011 %T Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States %A Chitambar, Eric %A Carl Miller %A Shi, Yaoyun %K matrix polynomials %K Schwartz-Zippel lemma %K unitary transformations %X

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.

%B Quantum Information and Computation %V 11 %P 813–819 %8 2001/09/01 %G eng %U http://dl.acm.org/citation.cfm?id=2230936.2230942 %N 9-10