Protecting cyclic controlled remote preparation of qudit states in a chain network
Si Jin, Song-Ya Ma, Yu Lu · Journal of Physics A Mathematical and Theoretical · 2025
Abstract We concern on the cyclic controlled remote preparation of qudit states in a chain network. By choosing proper entanglement resources, we first propose a unidirectional scheme where single-qudit states can be deterministically prepared clockwise among multiple users. Each sender executes a positive operator-value measure under the elaborately constructed basis and a projective measurement (PM) under the generalized X basis, while the controller carries out a PM under the generalized Z basis. The corresponding receiver can restore the target state by executing recovery operations which is deduced by universal formulas. Then, we present a bidirectional scheme such that each sender can prepare two single-qudit states in both clockwise and counterclockwise directions. It is worth stressing that network coding is applied at the controller’s site to reduce the classical communication cost. The schemes are further extended to arbitrary multi-particle systems. Additionally, we consider the impact of amplitude damping noise and phase damping noise, and employ the strategy of weak measurement to counteract noise.