Deciding unitary equivalence between matrix polynomials and sets of bipartite quantum states

Authors:
Eric Chitambar;Carl A. Miller;Yaoyun Shi
Affiliations:
Department of Physics, University of Toronto, Toronto, Ontario, Canada;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan
Venue:
Quantum Information & Computation
Year:
2011

Citing 3
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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.