Optimal exploitation of resource in remote state preparation

Morteza Nikaeen, Mehdi Ramezani, Alireza Bahrampour

Published 2020-03-21Version 1

The aim of this work is to characterize the transmission efficiency (TE) of remote state preparation (RSP) in terms of resource state parameters and then exploring the optimal resource of the protocol. To this end, the protocol is precisely modeled as an encoding-decoding mechanism that exploits the shared resource state to perform the RSP task. In this framework, the previous approaches to the problem are analyzed and improved. It is shown that contrary to the previous arguments, the quadratic fidelity, as well as linear fidelity, is a valid figure of merit to quantify the TE of RSP. Then, the performance of the protocol is evaluated in a fully optimized scenario which includes maximization over the encoding operators (restricted to the class of projective measurements) as well as a meaningful maximization over the decoding operators (restricted to the class of unitary operators). The results show that in this scenario, the TE in terms of both linear and quadratic fidelities scales with the sum of two largest eigenvalues of the squared correlation matrix of resource state that is zero only for product states. The advantages of the present approach compared with previous ones are also presented.