Teleportation of a qubit using entangled non-orthogonal states: A comparative study

TL;DR

This paper investigates how non-orthogonal entangled states affect quantum teleportation fidelity, comparing various quasi Bell states under ideal and noisy conditions to identify optimal channels and their robustness.

Contribution

It provides a detailed analysis of quasi Bell states as quantum channels for teleportation, including fidelity measures and noise effects, highlighting the dependence on non-orthogonality.

Findings

Optimal teleportation scheme using quasi Bell states is identified.

Performance varies with non-orthogonality and noise, affecting fidelity.

Certain quasi Bell states outperform others under specific noisy conditions.

Abstract

The effect of non-orthogonality of an entangled non-orthogonal state based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single qubit state using all the Bell type entangled non-orthogonal states known as quasi Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi Bell state is optimal. Further, the performance of various quasi Bell states as teleportation channel is compared in an ideal situation (i.e., in the absence of noise) and under different noise models (e.g., amplitude and phase damping channels). It is observed that the best choice of the quasi Bell state depends on the amount non-orthogonality, both in noisy and noiseless case. A specific quasi Bell state, which was found to be maximally entangled in the ideal conditions, is shown to be less efficient as a teleportation channel compared to other quasi Bell states in particular cases when subjected to noisy channels. It has also been observed that usually the value of average fidelity falls with an increase in the number of qubits exposed to noisy channels (viz., Alice's, Bob's and to be teleported qubits), but the converse may be observed in some particular cases.