Entanglement fidelity and measure of entanglement

TL;DR

This paper investigates the relationship between entanglement fidelity and various measures of entanglement, introducing new fidelities based on these measures and revealing limitations in their ability to detect entanglement preservation.

Contribution

It introduces new entanglement fidelities derived from different measures of entanglement and analyzes their association, highlighting the limitations of existing entanglement fidelity in detecting entanglement.

Findings

Entanglement fidelity is not directly associated with entanglement of formation, concurrence, or negativity.

New entanglement fidelities based on these measures are statistically compared with existing ones.

Existing entanglement fidelity cannot reliably detect entanglement preservation in quantum channels.

Abstract

The notion of entanglement fidelity is to measure entanglement preservation through quantum channels. Nevertheless, the amount of entanglement present in a state of a quantum system at any time is measured by quantities known as measures of entanglement. Since there are different types of measures of entanglement, one may expect an entanglement fidelity to associate with its own measure of entanglement counterpart. Here, we aim to investigate association between the so called entanglement fidelity and some measures of entanglement, namely, entanglement of formation, concurrence and negativity. New entanglement fidelities based upon these measures of entanglement are introduced and statistically compared with the so called previously introduced entanglement fidelity. It is shown that the entangling aspect of the so called entanglement fidelity is neither of type entanglement of formation and concurrence nor of type negativity. The results, in addition, expose inability of the so called entanglement fidelity for detecting, in a broad sense, entanglement preservation through quantum channels. Our analyses opens up a new venue in the study of entanglement fidelity and measure of entanglement by demonstrating that each measure of entanglement solely defines its own entanglement fidelity.