Joint remote state preparation (JRSP) of two-qubit equatorial state in quantum noisy channels

Abstract: This letter reports the influence of noisy channels on JRSP of two-qubit equatorial state. We present a scheme for JRSP of two-qubit equatorial state. We employ two tripartite Greenberger-Horne-Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We find the success probability to be $1/4$. However, this probability can be ameliorated to $3/4$ if the state preparers assist by transmitting individual partial information through classical channel to the receiver non-contemporaneously. Afterward, we investigate the effects of five quantum noises: the bit-flip noise, bit-phase flip noise, amplitude-damping noise, phase-damping noise and depolarizing noise on the JRSP process. We obtain the analytical derivation of the fidelities corresponding to each quantum noisy channel, which is a measure of information loss as the qubits are being distributed in these quantum channels. We find that the system loses some of its properties as a consequence of unwanted interactions with environment. For instance, within the domain $0<\lambda<0.65$, the information lost via transmission of qubits in amplitude channel is most minimal, while for $0.65<\lambda\leq1$, the information lost in phase flip channel becomes the most minimal. Also, for any given $\lambda$, the information transmitted through depolarizing channel has the least chance of success.