Deterministic hierarchical remote state preparation of a two-qubit entangled state using Brown et al. state in a noisy environment

Quantum communication is one of the cutting-edge research areas today, where the scheme of remote state preparation (RSP) has drawn significant attention of researchers. The authors propose here a hierarchical RSP protocol for sending a two-qubit entangled state using a seven-qubit highly entangled state derived from Brown et al. state. They have also studied here the effects of two well-known noise models namely amplitude damping (AD) and phase damping (PD). An investigation on the variation of the fidelity of the state with respect to the noise operator and receiver is made. PD noise is found to affect the fidelity more than the AD noise. Furthermore, the higher power receiver obtains the state with higher fidelity than the lower power receiver under the effect of noise. To the best of their knowledge, they believe that they have achieved the highest fidelity for the higher power receiver, 0.89 in the presence of maximum AD noise and 0.72 in the presence of maximum PD noise, compared to all the previously proposed RSP protocols in noisy environments. The study of noise is described in a very pedagogical manner for a better understanding of the application of noise models to a communication protocol.