# Tri-partite non-maximally entangled mixed states as a resource for optimum controlled quantum teleportation fidelity

## TL;DR

This paper investigates how specific three-qubit mixed states, particularly non-maximally entangled mixed X states, can optimize controlled quantum teleportation fidelity, challenging previous assumptions about maximally entangled states.

## Contribution

It identifies non-maximally entangled mixed X states as optimal resources for controlled quantum teleportation, contrary to the belief that maximally entangled states are always best.

## Key findings

- X-NMEMs achieve optimal teleportation fidelity for given entanglement and mixedness.
- X-MEMS do not always achieve maximum fidelity, contradicting traditional views.
- Biseparable X-NMEMs can be effective resources for high-fidelity teleportation.

## Abstract

Three-qubit mixed states are used as a channel for controlled quantum teleportation (CQT) of single-qubit states. The connection between different channel parameters to achieve maximum controlled teleportation fidelity is investigated. We show that for a given multipartite entanglement and mixedness, a class of non-maximally entangled mixed $X$ states ($X-$NMEMS) achieves optimum controlled quantum teleportation fidelity, interestingly a class of maximally entangled mixed $X$ states ($X-$MEMS) fails to do so. This demonstrates, for a given spectrum and mixedness, that $X-$MEMS are not sufficient to attain optimum controlled quantum teleportation fidelity, which is in contradiction with the traditional quantum teleportation of single qubits. In addition, we show that biseparable $X-$NMEMS, for a certain range of mixedness, are useful as a resource to attain high controlled quantum teleportation fidelity, which essentially lowers the requirements of quantum channels for CQT.