@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} }