Hierarchical Joint Remote State Preparation in Noisy Environment

TL;DR

This paper introduces a hierarchical joint remote state preparation protocol using 5-qubit cluster states, analyzing its robustness under various noise models and proposing a probabilistic version for practical quantum communication.

Contribution

It presents a novel hierarchical JRSP scheme with noise analysis and a probabilistic variant, advancing secure quantum communication methods.

Findings

Higher power agents achieve better fidelity under amplitude and phase damping noise.

The protocol's robustness varies with noise type, affecting different hierarchy levels differently.

A probabilistic scheme using non-maximally entangled states is also proposed.

Abstract

A novel scheme for quantum communication having substantial applications in practical life is designed and analyzed. Specifically, we have proposed a hierarchical counterpart of the joint remote state preparation (JRSP) protocol, where two senders can jointly and remotely prepare a quantum state. One sender has the information regarding amplitude, while the other one has the phase information of a quantum state to be jointly prepared at the receiver's port. However, there exists a hierarchy among the receivers, as far as powers to reconstruct the quantum state is concerned. A 5-qubit cluster state has been used here to perform the task. Further, it is established that the proposed scheme for hierarchical JRSP (HJRSP) is of enormous practical importance in critical situations involving defense and other sectors, where it is essential to ensure that an important decision/order that can severely affect a society or an organization is not taken by a single person, and once the order is issued all the receivers don't possess an equal right to implement it. Further, the effect of different noise models (e.g., amplitude damping (AD), phase damping (PD), collective noise and Pauli noise models) on the HJRSP protocol proposed here is investigated. It is found that in AD and PD noise models a higher power agent can reconstruct the quantum state to be remotely prepared with higher fidelity than that done by the lower power agent(s). In contrast, the opposite may happen in the presence of collective noise models. We have also proposed a scheme for probabilistic HJRSP using a non-maximally entangled 5-qubit cluster state.