Estimating entanglement monotones with a generalization of the Wootters formula

TL;DR

This paper generalizes Wootters' formula to estimate entanglement monotones like concurrence in higher-dimensional and multipartite quantum systems, providing stronger criteria and identifying new bound entangled states.

Contribution

It introduces a generalized approach to compute lower bounds on concurrence, extending Wootters' formula beyond two qubits, and enhances entanglement detection methods.

Findings

Provides lower bounds on concurrence for complex systems

Identifies stronger bipartite entanglement criteria

Reveals new families of bound entangled states

Abstract

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 to recognize novel families of multiparticle bound entangled states.