Gain in Performance of Teleportation with Uniformity-breaking Distributions

TL;DR

This paper investigates how non-uniform prior information about input states improves quantum teleportation fidelity and reduces classical communication needs, especially in higher dimensions, by analyzing polar cap and von Mises-Fisher distributions.

Contribution

It introduces the use of non-uniform distributions to quantify prior information's role in enhancing teleportation performance and compares their effectiveness.

Findings

Average fidelity increases with more input information.

Polar cap distribution yields smaller deviation than von Mises-Fisher.

Classical communication decreases as prior information increases.

Abstract

Prior information about the input state can be utilized to enhance the efficiency of quantum teleportation which we quantify using the first two moments of fidelity. The input knowledge is introduced by relaxing the uniformity assumption in the distribution of the input state and considering non-uniform distributions, namely the polar cap and von Mises-Fisher densities. For these distributions,we show that the average fidelity increases while the deviation decreases with the increase of information content about the input ensemble thereby establishing its role as a resource. Our comparative study between these two distributions reveals that for the same amount of information content about inputs, although the average fidelity yield is the same for both, the polar cap distribution is "better" as it offers a smaller deviation. Moreover, we contrast the resource of prior information with other resources involved in the protocol like shared entanglement and classical communication. Specifically, we observe that unlike uniform distribution, the amount of classical communication required to fulfill the task decreases with the increase of information available for inputs. We also investigate the role of prior information in higher (three) dimensional teleportation and report the signatures of dimensional advantage in prior information-based teleportation.