Entanglement witness operator for quantum teleportation

TL;DR

This paper introduces a hermitian witness operator that can identify quantum states suitable for teleportation by analyzing their fully entangled fraction, aiding in the detection of useful entangled resources.

Contribution

The paper demonstrates that the set of states capable of teleportation is convex and compact, enabling the construction of witness operators for identifying useful entangled states.

Findings

The set of states with sufficient fully entangled fraction is convex and compact.

A specific hermitian witness operator can distinguish states useful for teleportation.

Example applications of the witness operator are provided for different state classes.

Abstract

The ability of entangled states to act as resource for teleportation is linked to a property of the fully entangled fraction. We show that the set of states with their fully entangled fraction bounded by a threshold value required for performing teleportation is both convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states useful for performing teleportation. We present an example of such a witness operator illustrating it for different classes of states.