Simulated annealing and entanglement of formation for $(n\ensuremath{\bigotimes}m)$-dimensional mixed states

Simulated annealing and entanglement of formation for $(n \otimes m)$ -dimensional mixed states

S. Allende, D. Altbir, and J. C. Retamal

Phys. Rev. A 92, 022348 – Published 24 August 2015

Abstract

The simulated annealing algorithm, a method commonly used to calculate properties of condensed-matter systems, is used to calculate entanglement of formation for higher-dimensional mixed states. The method relies on representing a mixed state as a pure state in an enlarged Hilbert space, and on the search for the extension minimizing the convex roof of entanglement of formation. Exact results are found, and predictions for system reservoir dynamics in higher dimensions are confirmed. These findings open the way for new applications of the method in quantum information.