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Laser Physics

Hierarchical quantum communication of a single-qubit state with multiple users

Miao Liu, Nueraminaimu Maihemuti, Jiayin Peng, Yimamujiang Aisan, Jiangang Tang

Published Mar 10, 2025• 3 citations
Publisher

Abstract

Abstract The purpose of this article is to study hierarchical sharing with multiple users. Firstly, a genuine five-qubit entangled state is used as a quantum channel to achieve deterministic hierarchical sharing of an arbitrary unknown single-qubit state. In this setup, two agents of Alice, Bob and Charlie are at a higher power level in terms of accessing information, while the other two agents, namely David and Ellen, are at a lower power level. This scheme is then extended to the case of a non-maximally entangled five-qubit quantum channel. Secondly, we propose a scheme for remote state preparation of a known single-qubit state through a genuine five-qubit entangled state. In this scheme, the three agents of the senders Alice and Bob are divided into two different levels: Charlie at the higher level and David and Ellen at the lower level, and this scheme is further generalized to the case of non-maximally entangled five-qubit channels. Finally, the aforementioned schemes are generalized to the case involving m + n users. Here, the m + n agents of each generalized scheme are classified into two layers: m agents are at the higher power level, and n agents are at the lower power level.

DOI
10.1088/1555-6611/adbad1

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Abstract The purpose of this article is to study hierarchical sharing with multiple users. Firstly, a genuine five-qubit entangled state is used as a quantum channel to achieve deterministic hierarchical sharing of an arbitrary unknown single-qubit state. In this setup, two agents of Alice, Bob and Charlie are at a higher power level in terms of accessing information, while the other two agents, namely David and Ellen, are at a lower power level. This scheme is then extended to the case of a non-maximally entangled five-qubit quantum channel. Secondly, we propose a scheme for remote state preparation of a known single-qubit state through a genuine five-qubit entangled state. In this scheme, the three agents of the senders Alice and Bob are divided into two different levels: Charlie at the higher level and David and Ellen at the lower level, and this scheme is further generalized to the case of non-maximally entangled five-qubit channels. Finally, the aforementioned schemes are generalized to the case involving m + n users. Here, the m + n agents of each generalized scheme are classified into two layers: m agents are at the higher power level, and n agents are at the lower power level.
Abstract Recent studies have demonstrated the critical role of hierarchical quantum operation sharing in enhancing security and efficiency within quantum information systems. This approach enables the structured distribution of quantum operations among multiple parties, facilitating collaborative tasks essential for various practical applications. In this paper, we explore the hierarchical sharing of a partially known single-qubit operation, and propose a four-party hierarchical sharing scheme utilizing a non-maximally entangled six-qubit state as the quantum channel. This scheme can be regarded as two sub-schemes, wherein three agents are divided into two power levels for information access: one at a higher power level and the other at a lower level. Each agent can reconstruct the target state with complete certainty, independent of the coefficients of the non-maximally entangled channel, through the cooperation of some or all other agents. Additionally, we extend this framework to accommodate m + n agents, where n agents operate at the higher power level while the remaining m agents function at the lower power level.
A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled |χ〉 state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice's secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.
A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X） state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice＇s secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.
Abstract This paper puts forward a novel hierarchical controlled asymmetric bidirectional hybrid quantum communication scheme that can be applied to hierarchical quantum information transmission tasks in various application scenarios. In this scheme, with only Charlie’s assistance, Alice can accomplish the less crucial task of remotely preparing any single-qubit state for Bob. Simultaneously, Bob aims to transmit any two-qubit states to Alice via quantum teleportation. As a more vital communication task, apart from obtaining the consent of the control agent Charlie, Bob also requires the help of another control agent, David. Only with the combined control and support of Charlie and David can this task be successfully completed by Bob. In an ideal environment, the success rate of this protocol is 1. Given that noise is inevitable in practical communication, this paper further investigates the impact of different noises on this communication scheme and analyzes and compares its efficiency with other existing similar schemes. The proposed protocol outperforms existing hierarchical quantum communication solutions in terms of task generality and flexibility. By assigning different levels of controllers to different tasks, it provides users with greater flexibility to meet their specific needs, especially in scenarios requiring both multi-level authorization control and hybrid quantum communication.
With the emergence of classical communication security problems, quantum communication has been studied more extensively. In this paper, a novel probabilistic hierarchical quantum information splitting protocol is designed by using a non-maximally entangled four-qubit cluster state. Firstly, the sender Alice splits and teleports an arbitrary one-qubit secret state invisibly to three remote agents Bob, Charlie, and David. One agent David is in high grade, the other two agents Bob and Charlie are in low grade. Secondly, the receiver in high grade needs the assistance of one agent in low grade, while the receiver in low grade needs the aid of all agents. While introducing an ancillary qubit, the receiver’s state can be inferred from the POVM measurement result of the ancillary qubit. Finally, with the help of other agents, the receiver can recover the secret state probabilistically by performing certain unitary operation on his own qubit. In addition, the security of the protocol under eavesdropping attacks is analyzed. In this proposed protocol, the agents need only single-qubit measurements to achieve probabilistic hierarchical quantum information splitting, which has appealing advantages in actual experiments. Such a probabilistic hierarchical quantum information splitting protocol hierarchical is expected to be more practical in multipartite quantum cryptography.
Abstract This article proposes an asymmetric bidirectional hierarchical quantum teleportation protocol, which is based on a quantum channel composed of a maximum of eight-qubit entangled state. With this method, Alice can transmit an unknown single-qubit state to Bob, meanwhile, Bob can transmit an arbitrary unknown two-qubit quantum state to Alice. As a sender with high authority, Bob can send any unknown two-qubit quantum state to Alice only under the sole control of the controller Charlie; Alice, as a sender with low-level permissions, if Bob intends to receive the unknown single-qubit quantum state sent by Alice, he must get the permission and assistance of Charlie and David to complete the communication.