Evaluation of convex roof entanglement measures

TL;DR

This paper introduces a versatile method for calculating convex roof entanglement measures applicable to various quantum states, enabling efficient computation of entanglement quantifiers and bounds with practical examples.

Contribution

The authors develop a general approach to compute convex roof entanglement measures for states where pure state measures are polynomial functions of expectation values, including new methods for several entanglement measures.

Findings

Efficient computation of linear entropy of entanglement and assistance measures.

Bounding the dimension of entanglement in bipartite systems.

Application to three-tangle and device-independent entanglement quantification.

Abstract

We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples