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Convex Roof Optimization from Cartan Decompositions

Peter Love, Haverford College

(Session 10c : Saturday from 5:00pm-5:30pm)

Abstract. Extension of pure state entanglement measures to mixed states requires optimization over the set of ensembles that realize the density matrix. As discovered independently by Schroedinger, Jaynes and Hughston, Josza and Wooters, all ensembles may be realized by a unitary transformation of an initial ensemble. Hence the convex roof extension of pure state entanglement may be phrased as a problem of optimization on the unitary group. Prior work on this problem has used an Euler-Hurwitz parameterization of the unitary group. In this work, we describe the use of a parameterization based on a pair of Cartan decompositions previously developed in the context of the quantum Shannon decomposition.