TY - JOUR T1 - Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States JF - Quantum Information and Computation Y1 - 2011 A1 - Chitambar, Eric A1 - Carl Miller A1 - Shi, Yaoyun KW - matrix polynomials KW - Schwartz-Zippel lemma KW - unitary transformations AB -

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.

VL - 11 U4 - 813–819 UR - http://dl.acm.org/citation.cfm?id=2230936.2230942 CP - 9-10 ER -