Sensitivity of entanglement measures in bipartite pure quantum states

TL;DR

This paper compares four entanglement measures for bipartite pure states, analyzing their sensitivity and partial order, and demonstrates their use in tracking entanglement dynamics in a simple quantum model.

Contribution

It investigates the partial order and sensitivity of four entanglement measures, revealing their relative responsiveness to quantum entanglement and practical application in dynamic entanglement monitoring.

Findings

Concurrence has the highest sensitivity to entanglement.

Schmidt number has the lowest sensitivity.

Measures can track entanglement dynamics in a two-qutrit model.

Abstract

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based on Schmidt decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability.