Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States

TitleDeciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States
Publication TypeJournal Article
Year of Publication2011
AuthorsChitambar, E, Miller, C, Shi, Y
JournalQuantum Information and Computation
Volume11
Issue9-10
Pages813–819
Date Published2001/09/01
ISSN1533-7146
Keywordsmatrix polynomials, Schwartz-Zippel lemma, unitary transformations
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.

URLhttp://dl.acm.org/citation.cfm?id=2230936.2230942