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Physica Scripta

Enhancing hierarchical remote preparation of an arbitrary n-qudit equatorial state by weak measurement and measurement reversal

Xia Yan, Song-Ya Ma, Si Jin

Published Apr 5, 2024• 10 citations
Publisher

Abstract

Abstract Based on the demand for safer and more efficient quantum network communication, we propose two deterministic protocols to achieve the remote preparation of an arbitrary n-qudit equatorial states among multiple agents by selecting appropriate entanglement resources. The level of the agents varies depending on their authorities to restore the secret state. The superior agent requires the cooperation of the residual superior agents and any one of the subordinate agents, while the subordinate agent needs the help of all the other agents. To be emphasized, the recovery operations are deduced by general formulas that distinctly elucidate their relevance with the measurement outcomes. Additionally, we discuss the impact of amplitude damping noise and utilize weak measurement and measurement reversal to suppress noise.

DOI
10.1088/1402-4896/ad3b44

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Abstract Based on the demand for safer and more efficient quantum network communication, we propose two deterministic protocols to achieve the remote preparation of an arbitrary n-qudit equatorial states among multiple agents by selecting appropriate entanglement resources. The level of the agents varies depending on their authorities to restore the secret state. The superior agent requires the cooperation of the residual superior agents and any one of the subordinate agents, while the subordinate agent needs the help of all the other agents. To be emphasized, the recovery operations are deduced by general formulas that distinctly elucidate their relevance with the measurement outcomes. Additionally, we discuss the impact of amplitude damping noise and utilize weak measurement and measurement reversal to suppress noise.
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Considering the difference in the ability of agents to prepare target state and the highly entangled nature of the Brown state, we propose a hierarchical remote preparation scheme to prepare an arbitrary two-qubit state via Brown state. There are four agents who are classified into two grades with respect to their abilities of restoring the target state. The upper-grade agent can accomplish the task with the help of any two remaining agents. While the agent at the lower grade requires the cooperation of all the other agents. Compared with previous hierarchical remote preparation schemes for an arbitrary two-qubit state, our scheme offers enhanced security by necessitating the collaboration of at least two other agents for any single agent to prepare the target state. It is worth mentioning that the recovery operation of an agent, whether he is of upper or lower grade, can be derived from the general expression, which clearly reveals the relationship with the measurement results. Moreover, we extend the proposed scheme to the case of an arbitrary multi-qubit state, thereby enhancing the capacity for quantum information transfer. Additionally, we evaluated the impact of amplitude-damping noise and phase-damping noise on the proposed scheme.
Based on Jin et al.’s hierarchical remote preparation scheme of an arbitrary [Formula: see text]-qudit state with three agents, we propose one scheme for multiple agents by utilizing the symmetry of cluster states. To save entanglement resource, we then put forward the other improved scheme. There exists a hierarchy among the agents in terms of their abilities which are quantified by nonconditioned fidelity. The upper-grade agent needs the assistance of all the remaining upper-grade agents and any one of the lower-grade agents to recover the target state, while the lower-grade agent requires all the other agents’ collaboration. It is important to emphasize that the recovery operation is derived by a general expression clearly revealing the relationship with the measurement results.
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.
Abstract By elaborately selecting entangled channel, we put forward a universal scheme to achieve bidirectional remote preparation of qudit states with arbitrary numbers of particles under the control of the supervisor. Each sender needs to perform a positive-operator-value measurement and a projective measurement, while the supervisor requires to execute a projective measurement. Based on their measurement outcomes, the receivers can recover the desired states concurrently by carrying out single-qudit generalized Pauli operations which are given by general formulas. A point to highlight is that classical communication cost is greatly reduced at the supervisor’s broadcast channel by taking advantage of network coding. In addition, we analyze the influence of amplitude-damping and phase-damping noises, and utilize weak measurement and environment-assisted measurement to suppress noise.
Abstract We propose a protocol to Mentor initiated hierarchical joint remote prepare the arbitrary n-qudit state with generalized Bell states.The agents share generalized Bell states with the Mentor. The Mentor performs five-qudit projective measurements on his entangled particles to initiate the quantum channel shared by the agents. All the senders share the information of the prepared state and make quantum measurements on their particles based on the state to be prepared. The agent in the upper grade needs only the assistance of one of the agents in the lower grade to reconstruct the original state, while the agents in the lower grade need the assistance of all the other agents to recover the original state. It is more convenient in application than others since the agents in the protocol only requires two-particle entanglement for Mentor initiated hierarchical joint remote preparation of an arbitrary n-qudit state.