Entanglement thresholds for displaying the quantum nature of teleportation

TL;DR

This paper investigates the conditions under which quantum teleportation using noisy X-state channels exhibits genuine quantum features, identifying entanglement thresholds and the impact of fidelity redistribution mechanisms.

Contribution

It introduces a fidelity redistribution scheme using unambiguous state extraction to analyze quantum features in noisy teleportation channels, revealing new entanglement thresholds.

Findings

Entanglement is necessary but not sufficient for quantum teleportation fidelity.

Fidelity redistribution can produce outcomes with quantum features even below initial thresholds.

Threshold concurrence for normalized fidelity can be lower than that for total fidelity.

Abstract

A protocol for transferring an unknown single qubit state has quantum features when the average fidelity of the outcomes is greater than 2/3. We use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the teleportation when the process is performed with an X-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the total average fidelity f_X to display quantum features, i.e., we find a threshold C_X for the concurrence of the channel. If the mechanism for redistributing fidelity is successfully applied then we find a filtrable outcome with normalized average fidelity f_{X,USE,0} greater than f_X. In addition, we find the threshold concurrence of the channel C_{X,USE,0} in order for the normalized average fidelity to display quantum features. Surprisingly, we find that the threshold concurrence C_{X,USE,0} can be lesser than C_X. Finally, we show that if the mechanism for redistributing fidelity fails then the respective filtrable outcome has average fidelity lesser than 2/3.