Hierarchical Quantum Information Splitting Of Arbitrary Multi-Qubit States With Multiparty

Quantum information splitting is a research branch of quantum secret sharing.Hierarchical quantum information splitting is a communication mode of asymmetric transmission of unknown quantum states between agents with different abilities.Agents are at different grades based on their ability to restore the target state,and agents designated as receiver can restore the secret state with the help of some or all other agents.Hierarchical quantum information splitting is widely concerned because of its more practical application and higher security.However,most existing protocols focus on single-or two-qubit states,and there are few protocols for arbitrary multi-qubit states.Therefore,it is of great significance to study the general protocol of hierarchical quantum information splitting for arbitrary multi-qubit states.In this paper,we study the hierarchical quantum information splitting protocol of arbitrary multi-qubit states by using the maximally entangled and non-maximally entangled cluster states as entanglement resources.The main results are as follows:1.Taking the maximally entangled cluster state as the quantum resource,a deterministic hierarchical quantum information splitting scheme for arbitrary multi-qubit states with multiple agents is designed.Furthermore,we investigated the effects of two types of decoherent noise.Compared with the previous deterministic hierarchical quantum information splitting protocol,our protocol is a universal protocol applicable to arbitrary multi-qubit states with multiple agents,providing a general expression for the recovery operator,which clearly reveals the relationship between the recovery operation and the measurement results.2.Due to the difficulty in preparing and maintaining maximally entangled states,using non-maximally entangled cluster states as quantum resources,a probabilistic hierarchical quantum information splitting scheme of multi-qubit states with multiple agents is designed and the success probability of the protocol are given.Compared with the previous probabilistic hierarchical quantum information splitting protocol,the multi-qubit positive definite value measurement operator is ingeniously constructed by using the Hadamard matrix.The protocol is applicable to the general case of arbitrary multi-qubit states with multiple agents,and derive the general formula of the recovery operator.3.Taking non-maximally entangled cluster states as quantum resources,a hierarchical quantum information splitting scheme without information loss is designed for the first time,which can be applied to arbitrary multi-qubit states between multiple agents.The sender first predicts through the prediction mechanism.Even if hierarchical quantum information splitting is predicted to fail,the information of the target state will not be lost.As long as there are sufficient quantum channel resources,predictions can be repeated.Compared with the previous hierarchical quantum information splitting scheme using non-maximally entanglement resources,our scheme ensures that the secret state will not be lost even if the protocol fails.