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

arXiv:2606.23082

An Efficient and Perfect Secret Sharing Scheme on a Class of Non-Maximal Quantum Access Structure

Lei Li, Zhi Li

quant-phSubmitted Jun 22, 2026• Announced Jun 23, 2026• 0 citations
v1 · Jun 22, 2026v2 · Aug 7, 2026
arXivHTMLPDF

Abstract

Quantum secret sharing is one of the core security technologies in the field of quantum communication. Aiming at the problems of high quantum resource consumption and the difficulty in balancing security and efficiency existing in current quantum secret sharing schemes under non-maximal quantum access structure(QAS), this paper focuses on the judgment criteria of non-maximal QAS and the construction methods of efficient and perfect quantum secret sharing schemes on a kind of non-maximal QAS, i.e. hyperstar with three hyperedges. Firstly, we characterizes the forbidden sets and intermediate sets within this non-maximal QAS, and provides a characterization for non-maximal QAS realizable by pure-state encoding. Secondly, the representative element QAS of hyperstar with three hyperedges is defined, which serves as a substructure of this hyperstar QAS, and belongs to non-maximal QAS. Furthermore, we propose a universal, efficient, and perfect quantum secret sharing scheme based on this hyperstar QAS using corresponding classical secret sharing scheme as an auxiliary. By deploying lightweight quantum resources to representative element access structures, the proposed scheme reduces the difficulty in quantum state preparation and distribution, and enhances its security and resource utilization efficiency.

Related papers

Quantum Secret Sharing Scheme on Hypercyclic Quantum Structures

Lei Li, Zhi Li

This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if and only if they can be classified into 12 non-isomorphic types under hypergraph isomorphism, and these hypercyclic quantum access structures encompass all four hyperstars with three hyperedges.In prior work, efficient and perfect quantum secret sharing schemes were constructed for hyperstar access structures with three hyperedges using single photons in d -dimensional quantum systems. These schemes correspond to classical perfect secret sharing schemes with optimal information rates. However, for hypercyclic access structures with three hyperedges, the method described above fails to yield classical perfect secret sharing schemes with optimal information rates. In this work, we explicitly construct classical perfect secret sharing schemes with optimal information rates for these access structures by combining Simmons' geometric method with Shamir's threshold scheme. Subsequently, we employ single photons in d-dimensional quantum systems to build perfect QSS schemes upon these classical constructions.We introduce the concept of idealized information rate for minimal access structures in perfect QSS schemes. By extending the notion of efficiency proposed by Cabello [Phys. Rev. Lett., vol. 85, no. 26, p. 5635, 2000] for quantum key distribution protocols to QSS, we define the efficiency of minimally authorized subsets. Furthermore, we establish the relationship between the efficiency of minimally authorized subsets and the idealized information rate of minimal access structures. Finally, we rigorously prove that the QSS schemes constructed in this work achieve the highest efficiency among existing solutions.

arXiv:2510.27466•Oct 31, 2025•0 citations

Computational Quantum Secret Sharing

Alper Çakan, Vipul Goyal, Chen-Da Liu-Zhang +1 more

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over twenty years ago, previous works focused only on existence of perfectly secure schemes, and the share size of the known schemes is exponential even for access structures computed by polynomial size monotone circuits. This stands in contrast to the classical case, where efficient computationally-secure schemes have been long known for all access structures in $\mathsf{monotone~P}$, and one can even obtain shares which are much shorter than the secret which is impossible with perfect security. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time QSS schemes under standard assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS required exponential share size. We also construct QSS schemes for which the size of the shares is significantly smaller than the size of the secret. As in the classical case, this is impossible with perfect security. We also use our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of access structures to $1.5^{n+o(n)}$, improving upon best known schemes and matching the best known result for general access structures in the classical case. Finally, we show construct efficient schemes for all access structures in $\mathsf{P}$ and $\mathsf{NP}$ when the quantum secret sharing scheme is given multiple of copies of the secret.

arXiv:2305.00356•Apr 29, 2023•1 citation

Quantum Access Structure and Secret Sharing

Chen‐Ming Bai, Zhihui Li, Yongming Li

In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access structure, which shows the relationship between the number of minimal authorized sets and that of the players. Moreover, we investigate the construction of efficient quantum secret schemes by using these techniques, a decomposition and minimal maximal quantum access structure. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. For these quantum access structures, we present two quantum secret schemes via the idea of concatenation or a decomposition of a quantum access structure. As a consequence, the application of these techniques allow us to save more quantum shares and reduce more cost than the existing scheme.

arXiv:1701.01951•Jan 8, 2017•0 citations

Verifiable quantum secret sharing scheme using Bell states for a class of special access structures

Chen‐Ming Bai, Sujuan Zhang, Lu Liu

Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography. The existing QSS protocols are either [Formula: see text]-threshold or [Formula: see text]-threshold access structure, where [Formula: see text] denotes the number of players and [Formula: see text] denotes the threshold number of players. Here, we introduce a novel verifiable QSS scheme that executes a restricted hyperstar access structure by using entangled states. Our method involves encoding selected quantum states and their corresponding measurements to yield outcomes of either [Formula: see text] or [Formula: see text]. Furthermore, we give the validation of the scheme through the system of equations derived from the measurements, which then guarantees the honesty of the participants. At last, we also analyze the security of our scheme in two primary quantum attacks, such as external attacks and internal attacks.

International Journal of Quantum Information•Aug 23, 2024•5 citations

Construction of a Class of Communication-Efficient Quantum Secret Sharing Schemes

Chenhao Li, Zhihui Li, Jiansheng Guo +2 more

Quantum secret sharing is a fundamental technique in quantum cryptography. However, in practical quantum networks, it still faces several bottlenecks, such as high quantum communication cost and low transmission efficiency. To reduce the communication cost, ramp quantum secret sharing schemes have been proposed in existing studies. Nevertheless, intermediate sets in such schemes may leak partial information about the secret. To address this problem, this paper presents a method for detecting intermediate sets. Based on this method, we further propose a communication-efficient perfect quantum secret sharing scheme with eavesdropping detection capability.We analyze the communication cost under different numbers of participating parties and determine the range of participants that minimizes the reconstruction communication cost. The results verify the communication efficiency and security of the proposed scheme.

quant-pharXiv:2607.19891•Entropy•Jul 23, 2026•0 citations

Quantum secret sharing protocol using special entangled states for hyperstar access structure

Chen‐Ming Bai, Ya‐Xi Shu, Su-Juan Zhang

In this paper, drawing upon quantum state masking theory, we first propose a method that utilizes d-dimensional orthogonal arrays to encode quantum states into a multi-party quantum system. Building upon this foundation, we then design a quantum secret sharing scheme whose security is rooted in the principles of quantum information masking. This scheme is designed based on the hyperstar structure to define the access structure. Additionally, the protocol enables the transmission of arbitrary d-dimensional quantum states through quantum channels constructed using orthogonal arrays, ensuring that only participants within the access structure can recover the secret. We have thoroughly analyzed the security of this scheme against major quantum attacks, including intercept-resend attacks, entangle-measure attacks, and dishonest participant attack. In conclusion, our analysis examines the impact of four common types of noise on this protocol, confirming its immunity to dit-flip noise. Furthermore, we present a comparative analysis of the proposed scheme against existing quantum secret sharing protocols, highlighting its respective advantages.

Modern Physics Letters A•Feb 6, 2026•1 citation
Quantum secret sharing is one of the core security technologies in the field of quantum communication. Aiming at the problems of high quantum resource consumption and the difficulty in balancing security and efficiency existing in current quantum secret sharing schemes under non-maximal quantum access structure(QAS), this paper focuses on the judgment criteria of non-maximal QAS and the construction methods of efficient and perfect quantum secret sharing schemes on a kind of non-maximal QAS, i.e. hyperstar with three hyperedges. Firstly, we characterizes the forbidden sets and intermediate sets within this non-maximal QAS, and provides a characterization for non-maximal QAS realizable by pure-state encoding. Secondly, the representative element QAS of hyperstar with three hyperedges is defined, which serves as a substructure of this hyperstar QAS, and belongs to non-maximal QAS. Furthermore, we propose a universal, efficient, and perfect quantum secret sharing scheme based on this hyperstar QAS using corresponding classical secret sharing scheme as an auxiliary. By deploying lightweight quantum resources to representative element access structures, the proposed scheme reduces the difficulty in quantum state preparation and distribution, and enhances its security and resource utilization efficiency.
This paper investigates the construction of efficient quantum secret sharing schemes for quantum access structures based on hypergraphs with three hyperedges. We prove that hypercycles with three hyperedges are quantum access structures if and only if they can be classified into 12 non-isomorphic types under hypergraph isomorphism, and these hypercyclic quantum access structures encompass all four hyperstars with three hyperedges.In prior work, efficient and perfect quantum secret sharing schemes were constructed for hyperstar access structures with three hyperedges using single photons in d -dimensional quantum systems. These schemes correspond to classical perfect secret sharing schemes with optimal information rates. However, for hypercyclic access structures with three hyperedges, the method described above fails to yield classical perfect secret sharing schemes with optimal information rates. In this work, we explicitly construct classical perfect secret sharing schemes with optimal information rates for these access structures by combining Simmons' geometric method with Shamir's threshold scheme. Subsequently, we employ single photons in d-dimensional quantum systems to build perfect QSS schemes upon these classical constructions.We introduce the concept of idealized information rate for minimal access structures in perfect QSS schemes. By extending the notion of efficiency proposed by Cabello [Phys. Rev. Lett., vol. 85, no. 26, p. 5635, 2000] for quantum key distribution protocols to QSS, we define the efficiency of minimally authorized subsets. Furthermore, we establish the relationship between the efficiency of minimally authorized subsets and the idealized information rate of minimal access structures. Finally, we rigorously prove that the QSS schemes constructed in this work achieve the highest efficiency among existing solutions.
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over twenty years ago, previous works focused only on existence of perfectly secure schemes, and the share size of the known schemes is exponential even for access structures computed by polynomial size monotone circuits. This stands in contrast to the classical case, where efficient computationally-secure schemes have been long known for all access structures in monotone P\mathsf{monotone~P}monotone P, and one can even obtain shares which are much shorter than the secret which is impossible with perfect security. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time QSS schemes under standard assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS required exponential share size. We also construct QSS schemes for which the size of the shares is significantly smaller than the size of the secret. As in the classical case, this is impossible with perfect security. We also use our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of access structures to 1.5n+o(n)1.5^{n+o(n)}1.5n+o(n), improving upon best known schemes and matching the best known result for general access structures in the classical case. Finally, we show construct efficient schemes for all access structures in P\mathsf{P}P and NP\mathsf{NP}NP when the quantum secret sharing scheme is given multiple of copies of the secret.
In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access structure, which shows the relationship between the number of minimal authorized sets and that of the players. Moreover, we investigate the construction of efficient quantum secret schemes by using these techniques, a decomposition and minimal maximal quantum access structure. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. For these quantum access structures, we present two quantum secret schemes via the idea of concatenation or a decomposition of a quantum access structure. As a consequence, the application of these techniques allow us to save more quantum shares and reduce more cost than the existing scheme.
Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography. The existing QSS protocols are either [Formula: see text]-threshold or [Formula: see text]-threshold access structure, where [Formula: see text] denotes the number of players and [Formula: see text] denotes the threshold number of players. Here, we introduce a novel verifiable QSS scheme that executes a restricted hyperstar access structure by using entangled states. Our method involves encoding selected quantum states and their corresponding measurements to yield outcomes of either [Formula: see text] or [Formula: see text]. Furthermore, we give the validation of the scheme through the system of equations derived from the measurements, which then guarantees the honesty of the participants. At last, we also analyze the security of our scheme in two primary quantum attacks, such as external attacks and internal attacks.
Quantum secret sharing is a fundamental technique in quantum cryptography. However, in practical quantum networks, it still faces several bottlenecks, such as high quantum communication cost and low transmission efficiency. To reduce the communication cost, ramp quantum secret sharing schemes have been proposed in existing studies. Nevertheless, intermediate sets in such schemes may leak partial information about the secret. To address this problem, this paper presents a method for detecting intermediate sets. Based on this method, we further propose a communication-efficient perfect quantum secret sharing scheme with eavesdropping detection capability.We analyze the communication cost under different numbers of participating parties and determine the range of participants that minimizes the reconstruction communication cost. The results verify the communication efficiency and security of the proposed scheme.
In this paper, drawing upon quantum state masking theory, we first propose a method that utilizes d-dimensional orthogonal arrays to encode quantum states into a multi-party quantum system. Building upon this foundation, we then design a quantum secret sharing scheme whose security is rooted in the principles of quantum information masking. This scheme is designed based on the hyperstar structure to define the access structure. Additionally, the protocol enables the transmission of arbitrary d-dimensional quantum states through quantum channels constructed using orthogonal arrays, ensuring that only participants within the access structure can recover the secret. We have thoroughly analyzed the security of this scheme against major quantum attacks, including intercept-resend attacks, entangle-measure attacks, and dishonest participant attack. In conclusion, our analysis examines the impact of four common types of noise on this protocol, confirming its immunity to dit-flip noise. Furthermore, we present a comparative analysis of the proposed scheme against existing quantum secret sharing protocols, highlighting its respective advantages.