Entanglement and Teleportation in Bipartite System

TL;DR

This paper mathematically analyzes the original quantum teleportation protocol for mixed states, focusing on how the mixedness of the entangled channel affects teleportation performance.

Contribution

It provides a detailed formulation of teleportation with mixed states and identifies conditions under which maximally entangled mixed states serve as effective teleportation channels.

Findings

Maximally entangled mixed states with rank-4 can teleport single-qubit states when p1 > 0.5.

The effectiveness of teleportation depends on the mixedness parameter p1.

Discussion included cases where p1 ≤ 0.5, highlighting limitations.

Abstract

We present a mathematical formulation of old teleportation protocol (original teleportation protocol introduced by Bennett et.al.) for mixed states and study in detail the role of mixedness of the two qubit quantum channel in a teleportation protocol. We show that maximally entangled mixed state described by the density matrix of rank-4 will be useful as a two qubit teleportation channel to teleport a single qubit mixed state when the teleportation channel parameter p1 greater than 0.5. Also we discuss the case when p1 less than equal to 0.5.