03224nas a2200205 4500008004100000022001400041245009700055210006900152260001500221300001400236490000700250520257700257653002302834653002602857653002802883100002002911700001702931700001602948856005402964 2011 eng d a1533-714600aDeciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States0 aDeciding Unitary Equivalence Between Matrix Polynomials and Sets c2001/09/01 a813–8190 v113 a

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.

10amatrix polynomials10aSchwartz-Zippel lemma10aunitary transformations1 aChitambar, Eric1 aMiller, Carl1 aShi, Yaoyun uhttp://dl.acm.org/citation.cfm?id=2230936.2230942