Estimating Entanglement Monotones with a Generalization of the Wootters Formula

Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite systems. We demonstrate that for certain families of states our results constitute the strongest bipartite entanglement criterion so far; moreover, they allow us to recognize novel families of multiparticle bound entangled states.

Figure 1

Detecting entanglement in the Horodecki $3\times 3$ bound entangled state mixed with white noise. The criterion of Observation 1 (points denoted by OBS1) is stronger than previously known criteria. For values of $p$ smaller than the values given by SEP, the states ${\varrho }_a(p)$ are proven to be separable. See the text for further details.