Quantum entanglement and teleportation assisted by multiple parties

TL;DR

This paper proves the necessary and sufficient conditions for quantum teleportation involving multiple parties and extends the understanding of entanglement requirements for teleporting single-qubit messages.

Contribution

It provides a formal proof of the feasibility condition for quantum teleportation and generalizes the condition for multi-party scenarios.

Findings

Proof of the original feasibility condition for quantum teleportation

Extension of the condition to three-party and n-party systems

Clarification of entanglement requirements for multi-party teleportation

Abstract

Quantum teleportation can be performed if and only if a message is combined with a maximally entangled state. Bennett et al. originally claimed this feasibility condition. In this paper, I give a proof of that condition. Moreover, I specify the condition for teleportation when a single-qubit message is combined with a three-qubit state distributed among three parties. I also consider the situation that a single-qubit message is combined with an $n$-qubit state distributed among $n$ parties.