Analysis of control power in controlled remote state preparation schemes

TL;DR

This paper analyzes the control power in controlled remote state preparation, establishing bounds and criteria to evaluate the effectiveness of various protocols for preparing arbitrary quantum states.

Contribution

It introduces a lower bound on control power for D-dimensional states and assesses the suitability of existing protocols, highlighting the importance of controller entropy.

Findings

Controller's entropy should be at least log2 D bits for D-dimensional states.

Some non-maximally entangled channels are unsuitable for perfect control.

The criteria can evaluate other controlled quantum communication schemes.

Abstract

We quantify and analyze the controller's power in controlled remote state preparation schemes. Our analysis provides a lower bound on the control power required for controlled remote preparation of arbitrary D-dimensional states. We evaluate several existing controlled remote state preparation protocols and show that some proposed non-maximally entangled channels are not suitable for perfect controlled remote preparation of arbitrary quantum states from the con- troller's point of view. We find that for remotely preparing D-dimensional states, the entropy of each controller should be no less than log_2 D bits. Our criteria are not only useful for evaluating controlled remote state preparation schemes but can also be used for other controlled quantum communication schemes.