Abstract

Quantifying entanglement has been a longstanding goal of quantum information theory, and many measures for pure states exist. These measures may be extended to mixed states by the convex roof construction. This requires the determination of the convex decomposition of the density matrix into pure states that minimizes the average pure state entanglement. One may regard this as the mean pure-state entanglement cost of synthesizing the density matrix. This minimization is challenging, and exact solutions are only known in a few cases, the most famous of which is the concurrence for two qubits. The next hardest case would seem to be the three-tangle for mixed states of three qubits, for which an analytic form is currently unknown. In this talk I will describe numerical techniques to both compute and bound the three-tangle, and give some properties of the minimal ensembles for this and other polynomial entanglement monotones.