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Physica Scripta

Authenticated hierarchical quantum state sharing based on non-maximally entangled states

Tianai Zhou, Xiu‐Bo Chen, Gang Xu, Ying Guo

Published Aug 5, 2024• 4 citations
Publisher

Abstract

Abstract Hierarchical quantum state sharing (HQSTS) provides a way for the quantum state from one party to another among multiple parties asymmetrically. In the process, it is necessary to ensure the legitimacy and authenticity of participants to defend against attacks caused by neglecting authentication. Hence, we propose a three-phase probabilistic HQSTS protocol with identity authentication. Firstly, the legitimacy of participants is verified in the identity authentication phase, which effectively prevents impersonation and deception. Secondly, the sender Alice sends the target quantum state to three agents asymmetrically, which implies that there is a hierarchy of agents regarding their ability to recover the secret state. The high authority agent can recover the state without the cooperation of all agents, while the low authority agent has to recover the state with the cooperation of all agents. Thirdly, based on the non-maximally entangled cluster states, the sharing of the arbitrary three-qubit states is realized, which increases the amount of information transmitted. Using the Qiskit framework, the quantum circuit and simulation results for a particular case are given to verify the feasibility and correctness of our protocol. Moreover, the security of the protocol is analyzed from the perspective of both internal and external attacks.

DOI
10.1088/1402-4896/ad6b50

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Abstract Hierarchical quantum state sharing (HQSTS) provides a way for the quantum state from one party to another among multiple parties asymmetrically. In the process, it is necessary to ensure the legitimacy and authenticity of participants to defend against attacks caused by neglecting authentication. Hence, we propose a three-phase probabilistic HQSTS protocol with identity authentication. Firstly, the legitimacy of participants is verified in the identity authentication phase, which effectively prevents impersonation and deception. Secondly, the sender Alice sends the target quantum state to three agents asymmetrically, which implies that there is a hierarchy of agents regarding their ability to recover the secret state. The high authority agent can recover the state without the cooperation of all agents, while the low authority agent has to recover the state with the cooperation of all agents. Thirdly, based on the non-maximally entangled cluster states, the sharing of the arbitrary three-qubit states is realized, which increases the amount of information transmitted. Using the Qiskit framework, the quantum circuit and simulation results for a particular case are given to verify the feasibility and correctness of our protocol. Moreover, the security of the protocol is analyzed from the perspective of both internal and external attacks.
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.
Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements, and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement (POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.
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 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.
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.
Based on the teleportation by quantum walk, a quantum secret sharing scheme with credible authentication is proposed.Using the Hash function and quantum local operation, combined with the two-step quantum walks circuit on the line, the identity authentication and the teleportation of the secret information in distribution phase are realized.Participants collaborate honestly to recover secret information based on particle measurement results, preventing untrusted agents and external attacks from obtaining useful information.Due to the application of quantum walk, the sender does not need to prepare the necessary entangled state in advance, simply encodes the information to be sent in the coin state, and applies the conditional shift operator between the coin space and the position space to produce the entangled state necessary for quantum teleportation.Security analysis shows that the protocol can effectively resist intercept/resend attacks, entanglement attacks, participant attacks, and impersonation attacks.In addition, the quantum walk circuit used has been implemented in many different physical systems and experiments, so this quantum secret sharing scheme may be achievable in the future.