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 |
Volume | 11 |
Issue | 9-10 |
Pages | 813–819 |
Date Published | 2001/09/01 |
ISSN | 1533-7146 |
Keywords | matrix 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. |
URL | http://dl.acm.org/citation.cfm?id=2230936.2230942 |