A Comparison of Entanglement Measures Against Teleportation Fidelity

Entanglement is a quantum phenomenon characterized by non-classical correlations between two systems. It can be used as a resource in quantum tasks such as secure data encryption and high-fidelity teleportation. Quantifying entanglement remains an open question - there exist different measures of entanglement which agree on which states are maximally and minimally entangled, yet disagree on the entanglement ordering of some intermediate entangled states. We focus on three of these measures: concurrence, negativity, and relative entropy of entanglement. We show the relation between these three measures, including contradictions in the ordering of some quantum states. This leads to the hypothesis that these measures disagree because they are measuring distinct resources. To test this idea, we search for the existence of a teleportation resource by looking for a significant correlation between teleportation fidelity and one of these three measures of entanglement. Our analysis shows no clear distinction between any of these measures of entanglement. Further work will be required to solve the complex problem of entanglement quantification.