Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Laser Physics Letters

Deterministic hierarchical sharing of a partially known quantum operation via a non-maximally entangled state

Siqi Zhou, Nueraminaimu Maihemuti

Published Feb 5, 2025• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/adadda

Related papers

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

Miao Liu, Nueraminaimu Maihemuti, Jiayin Peng +2 more

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.

Laser Physics•Mar 10, 2025•3 citations

Hierarchical and probabilistic quantum state sharing via a non-maximally entangled stateHierarchical and probabilistic quantum state sharing via a non-maximally entangled stateHierarchical and probabilistic quantum state sharing via a non-maximally entangled state

彭家寅, 柏明强, 莫智文

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.

中国物理B：英文版•Jan 1, 2014•0 citations

Hierarchical and probabilistic quantum state sharing via a non-maximally entangled |χ〉 state

Peng Jia-yin, Ming-Qiang Bai, Zhiwen Mo

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.

Chinese Physics B•Jan 1, 2014•35 citations

Hierarchical and probabilistic quantum information splitting of an arbitrary two-qubit state via two cluster states

Wenming Guo, Lei-Ru Qin

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.

Chinese Physics B•Nov 1, 2018•21 citations

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

Tianai Zhou, Xiu‐Bo Chen, Gang Xu +1 more

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.

Physica Scripta•Aug 5, 2024•4 citations

Probabilistic Hierarchical Quantum Information Splitting of Arbitrary Multi-Qubit States

Jie Tang, Song-Ya Ma, Qi Li

By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.

Entropy•Aug 4, 2022•12 citations
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.
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.
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 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 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.
By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.