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 -