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arXiv:2512.22049 · IEEE International Symposium on Information Theory (ISIT)

Quantum Secret Sharing Rates

Gabrielle Lalou, Husein Natur, Uzi Pereg

quant-phcs.ITSubmitted Dec 26, 2025• Announced Dec 29, 2025• 0 citations
v1 · Dec 26, 2025v2 · Apr 26, 2026
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Abstract

This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. Following the approach of Zou et al. (2015) on classical secret sharing, we introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.

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This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. Following the approach of Zou et al. (2015) on classical secret sharing, we introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.
The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational (ZZZ) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.
Abstract The fundamental concept of secret sharing involves dividing a secret into multiple parts and distributing them among several participants, who collectively safeguard the secret. When it comes to restoring the secret, cooperation among specific participants is necessary to reconstruct the original secret. Quantum secret sharing (QSS) employs quantum methods to address some limitations of classical secret sharing. Semi-QSS, an advancement of quantum methods, requires fewer quantum resources. Previous semi-quantum protocols demanded at least one participant with full quantum capabilities and randomly generated secret information. This paper introduces a protocol allowing three participants lacking complete quantum capabilities to share secret information of specific bits with the assistance of a third party possessing complete quantum capabilities. Unlike previous approaches, this protocol does not require participants to possess full quantum capabilities and shares secret information of specific bits. These characteristics make the protocol more practical and flexible for real-world applications.
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security). While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply 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 n-party 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 setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.
Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum secret is distributed among a number of parties where some subsets of the parties are able to recover the secret while some subsets are unable to recover the secret. In the standard ((k, n)) quantum threshold secret sharing scheme, any subset of k or more parties out of the total n parties can recover the secret while other subsets have no information about the secret. But recovery of the secret incurs a communication cost of at least k qudits for every qudit in the secret. Recently, a class of communication efficient QSS schemes were proposed which can improve this communication cost to dd−k+1\frac{d}{{d - k + 1}}d−k+1d​ by contacting d ≥ k parties where d is fixed prior to the distribution of shares. In this paper, we propose a more general class of ((k, n)) quantum secret sharing schemes with low communication complexity. In these schemes the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n. This is the first such class of universal communication efficient quantum threshold schemes.
We present a fault-tolerate three-party quantum secret sharing (QSS) scheme over a collective-noise channel. Decoherence-free subspaces are used to tolerate two noise modes, a collective-dephasing channel and a collective-rotating channel, respectively. In this scheme, the boss uses two physical qubits to construct a logical qubit which acts as a quantum channel to transmit one bit information to her two agents. The agents can get the information of the private key established by the boss only if they collaborate. The boss Alice encodes information with two unitary operations. Only single-photon measurements are required to rebuilt Alice's information and detect the security by the agents Bob and Charlie, not Bell-state measurements. Moreover, Almost all of the photons are used to distribute information, and its success efficiency approaches 100% in theory.