Maximally entangled state and fully entangled fraction

TL;DR

This paper investigates maximally entangled states and introduces a generalized fully entangled fraction for d' imes d systems, providing conditions, properties, and applications in quantum teleportation.

Contribution

It generalizes the fully entangled fraction concept to d' imes d systems and offers criteria and witnesses for identifying maximally entangled and teleportation-useful states.

Findings

Necessary and sufficient conditions for maximally entangled states.

Definition of the fully entangled fraction in d' imes d systems.

Analysis of the fully entangled fraction's relation to quantum teleportation.

Abstract

We study maximally entangled states and fully entangled fraction in general d'\otimes d (d'\geq d) systems. Necessary and sufficient conditions for maximally entangled pure and mixed states are presented. As a natural generalization of the usual fully entangled fraction for d\otimes d systems, we define the maximal overlap between a given quantum state and the maximally entangled states as the fully entangled fraction in d'\otimes d systems. The properties of this fully entangled fraction and its relations to quantum teleportation have been analyzed. The witness for detecting maximally entangled states and quantum states that are useful for quantum teleportation is provided.