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Physica Scripta

Mentor initialed multiparty hierarchical joint remote preparation of an arbitrary n-qudit state via generalized Bell states

Rui-Heng Jing, Yu-Bin Huang, An-An Bi, Wenwen Luo, Ping Zhou, Qi Lan

Published Dec 21, 2023• 20 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad1801

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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.
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.
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.
The quantum equatorial state, a special kind of quantum state, has attracted much attention because of its potential for applications in quantum information processing. The remote preparations of arbitrary two-qudit, three-qudit equatorial and m-qudit equatorial states have been studied via different entangle quantum channels. In this paper, we propose two protocols for the controlled joint remote preparation of an arbitrary m-qudit equatorial state with a pure entangled quantum channel. The first is for the controlled joint remote preparation of the m-qudit equatorial state by using m multiparticle GHZ-class states as the quantum channel, and the second is for the controlled joint remote preparation of the m-qudit equatorial state via a multiparticle entangled state. All senders share information about the prepared state and perform m-particle projective measurements on their entangled particles according to their information about the prepared state. All controllers perform generalized X-basis measurements on their entangled particles. If a receiver cooperates with all the senders and controllers, he can prepare the original state probabilistically by performing unitary operations on his entangled particles and an auxiliary qubit. This protocol is more convenient for applications because it only requires nonmaximal entanglement for the controlled joint remote preparation of an arbitrary m-qudit equatorial state.
We present a general scheme for multiparty joint remote preparation of an arbitrary m -qudit state with a pure entangled quantum channel via positive operator-valued measurement (POVM). The n senders share the information of the prepared state. The first sender performs POVM on his particles according to his knowledge of the original state, the other n − 1 senders perform m -particle projective measurement and the receiver can probabilistically reconstruct the original state by performing unitary operations on his particles according to the senders' measurement results. The scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m -qudit state via pure entangled quantum states. Moreover, it discusses the relationship between the coefficients of the pure entangled states and the success probability.
We propose two protocols for joint, multi-party remote preparation of qudit states by using a d-level six-qudit Cluster state as the quantum channel. The first protocol is used for the joint remote preparation of an arbitrary two-qudit state via the d-level six-qudit Cluster state. The second is used for bi-directional joint remote preparation of an arbitrary single-qudit state via a d-level six-qudit Cluster state. All senders share information about the prepared state. The first sender applies Positive Operator-Valued Measurement (POVM) on her entangled particles in accordance with her information about the prepared state, while the second sender performs projective measurements in accordance with the information about the prepared state and the first sender’s measurement results. The receiver can prepare the original state by performing a corresponding unitary operation according to the measurement results from all the senders. These two protocols have the advantage of being able to provide a high channel capacity by using a d-level Cluster state as the quantum channel.
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.