A computable measure of entanglement

TL;DR

This paper introduces a computable entanglement measure for bipartite mixed states based on the partial transpose, defining the negativity $\mathcal{N}(\rho)$ and the logarithmic negativity $E_{\mathcal{N}}(\rho)$, and proves they are tractable to compute and do not increase under LOCC. It establishes LOCC monotonicity via a variational/bas e-norm framework and extends the construction to a family of related negativities. The authors then connect these measures to operational tasks: $\mathcal{N}$ provides a lower bound on the singlet-distance achievable by LOCC, yielding a bound on the teleportation distance, while $E_{\mathcal{N}}$ upper-bounds the distillable entanglement $E_D^{\epsilon}(\rho)$ for any $\epsilon<1$. They illustrate the approach with explicit calculations for pure states, highly symmetric states, and Gaussian states, and extend the framework to multipartite settings, defining several computable multipartite negativities and a hierarchical structure among them. The work offers a practical, broadly applicable entanglement proxy that supports quantitative analysis of entanglement resources in realistic, non-ideal quantum states and networks.

Abstract

We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.