Hierarchical Controlled Remote Preparation Of Equatorial States With Multiparty

Remote preparation of quantum states is a communication method which utilizes classical channel and quantum channel to transmit target state safely and efficiently.Remote preparation of quantum states without distance constraints allows for significant advances in connectivi-ty and communication,while improving the performance of telecommunications,computing,the internet and cryptography.Hierarchical controlled remote preparation has attracted wide attention because of its higher security compared with traditional remote preparation with sym-metrical agent power,considering the situation of different agent power in real life.However,hierarchical controlled remote preparation of equatorial states with higher clonal fidelity has not been studied.In this paper,hierarchical remote preparation of arbitrary single-qudit equatorial states are studied.1、Deterministic hierarchical controlled remote preparation protocol of single-qubit equa-torial states with four-qubit cluster states is proposed firstly.The sender can asymmetrically transmit the target state to any one of the three agents.A set of useful measurement bases is elaborately constructed which plays a key role in the protocol.Furthermore,a general proto-col with multiparty is designed by using the symmetry of cluster state.The main advantages are as follows:（1）a universal hierarchical controlled remote preparation protocol for arbitrary single-particle equatorial states between multiparty is proposed;（2）the general expression of the recovery operator is derived strictly,which clearly reveals the relationship with the mea-surement results;（3）the influence of high-dimensional noise is studied,and the fidelity is used to measure the closeness between the output state and the target state.2、Firstly,a hierarchical controlled remote preparation protocol of three-dimensional single-particle equatorial states using two four-qubit cluster states as quantum channel is designed.The success probability of the protocol is 75%.Then the protocol is extended to（9-dimensional equatorial states by9）qubit cluster states,and the scheme is extended to a more general case with multiparty.The main advantages are as follows:（1）considering the limitation that the high-dimensional entangled state is difficult to prepare,the degree mismatch problem is ap-plied to the protocol;（2）discussing the case of agents of different class and proposes a general protocol of probabilistic high-dimensional equatorial states between multiparty,which is deter-ministic if and only if(9=2⁹);（3）after rigorous derivation,the recovery operation of agents are given clearly.3、Adopting a multi-layer structure that ranks the sender.Firstly,three arbitrary single-qubit equatorial states are prepared remotely between three layers by nine-qubit entangled s-tates.The senders can be divided into three different levels due to the amount of control.The protocol is then extended to high-dimensional systems and a general protocol withlayers is designed.The main advantages are as follows:（1）the scheme adopts multi-layer hierarchi-cal structure;（2）The hierarchical controlled remote preparation of single-particle equatorial states with multiparty can be accomplished determinately;（3）the agents’recovery operation according to the measurement results are clearly given by rigorous calculation.