Faithful teleportation with arbitrary pure or mixed resource states

TL;DR

This paper systematically analyzes the conditions under which arbitrary pure or mixed entangled states can be used for faithful quantum teleportation, establishing necessary and sufficient criteria and exploring the role of entanglement.

Contribution

It provides the first comprehensive set of conditions for faithful teleportation using arbitrary entangled resource states, including mixed states, and clarifies the requirements for maximally entangled states.

Findings

Mixed states can enable perfect teleportation under specific conditions.

Maximally entangled pure states are necessary for certain teleportation scenarios.

Sender's measurements must be projectors onto maximally entangled states.

Abstract

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |\phi> in C^d with an entangled resource {\rho} in C^m \otimes C^d and C^d \otimes C^n are derived. It is shown that for {\rho} in C^m\otimesC^d, {\rho} must be a maximally entangled state, while for {\rho} in C^d \otimes C^n, {\rho} must be a puremaximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.