|Title||Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States|
|Publication Type||Journal Article|
|Year of Publication||2011|
|Authors||Chitambar, E, Miller, C, Shi, Y|
|Journal||Quantum Information and Computation|
|Keywords||matrix polynomials, Schwartz-Zippel lemma, unitary transformations|
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.