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Modern Physics Letters A

Hierarchical remote preparation of an arbitrary m-qudit state with multiple agents

Junli Jiang, Song-Ya Ma, Yan Xia

Published Oct 10, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1142/s0217732323501419

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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.
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Hierarchical remote preparation of equatorial states has practical applications but has not been studied before. We first propose a deterministic protocol for two-dimensional equatorial states via a four-qubit cluster state. The sender can asymmetrically transmit the secret state to any one of the three agents who are ranked in terms of their authorities. A set of useful measurement bases is elaborately constructed which plays a key role in the protocol. Then the protocol is generalized to high-dimensional system. Further, taking advantage of cluster state’s symmetry, we give a universal protocol with multiple agents. The high-grade agent needs the assistance of the remaining high-grade agents as well as one of the low-grade agents. While the low-grade agent needs the cooperation of all the other agents. The agents’ recovery operators are expressed by a general formula which clearly reveals the relationship with the measurement results. Additionally, the impact of two kinds of noise is analyzed.
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.
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.
By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.
We present a protocol for the hierarchical controlled joint remote implementation of the partially unknown operations of m qudits belonging to some restricted sets by using m multiparticle high-dimensional entangled states as the quantum channel. All the senders share the information of the partially unknown operations and cooperate with each other to implement the partially unknown operations on the remote receiver's quantum system. The receivers are hierarchized in accordance with their abilities to reconstruct the desired state. The agents in the upper grade need only cooperate with one of the lower-grade agents, and the agents in the lower grade need the cooperation of all the other agents. The protocol has the advantage of having high channel capacity by using a high-dimensional entangle state as the quantum channel for the hierarchial controlled joint remote implementation of partially unknown quantum operations of m qudits.