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arXiv:2511.05212

Revocation and Reconstruction of Shared Quantum States

Prakash Mudholkar, Chiranjeevi Vanarasa, Indranil Chakrabarty, Srinathan Kannan

quant-phSubmitted Nov 7, 2025• Announced Nov 10, 2025
v1 · Nov 7, 2025v2 · Nov 10, 2025
arXivHTMLPDF

Abstract

The problem of revocation of quantum states after sharing is interesting and we ask: Is it possible for a dealer to revoke the state once shared, before the reconstruction process? Additional resources like bell states are used to help the dealer to get back the state. In a three-party scenario, we show an independent way to revoke, if, for any reason, the dealer is not sure about the intention of the/any reconstructor. In general, the classical outcomes of the dealer in sharing phase are needed, to be able to reconstruct the state perfectly. When both the shareholders are dishonest, and without the dealer's knowledge, collude to reconstruct, they always have some chance of succeeding. This is addressed by giving more control to the dealer by making him/her) to have a quantum share as well. We give a sharing and revocation protocol with a four-qubit entangled resource shared among three parties (two qubits with the dealer and one each with the shareholders). We further consider a class of four qubit pure entangled states as resource and explicitly find the range of parameters for which the protocol will be successful.

DOI
10.1007/s11128-025-04951-y
Comments
arXiv admin note: substantial text overlap with arXiv:2112.15556

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The problem of revocation of quantum states after sharing is interesting and we ask: Is it possible for a dealer to revoke the state once shared, before the reconstruction process? Additional resources like bell states are used to help the dealer to get back the state. In a three-party scenario, we show an independent way to revoke, if, for any reason, the dealer is not sure about the intention of the/any reconstructor. In general, the classical outcomes of the dealer in sharing phase are needed, to be able to reconstruct the state perfectly. When both the shareholders are dishonest, and without the dealer's knowledge, collude to reconstruct, they always have some chance of succeeding. This is addressed by giving more control to the dealer by making him/her) to have a quantum share as well. We give a sharing and revocation protocol with a four-qubit entangled resource shared among three parties (two qubits with the dealer and one each with the shareholders). We further consider a class of four qubit pure entangled states as resource and explicitly find the range of parameters for which the protocol will be successful.
In this article we present a benchmark for resource characterization in the process of controlled quantum state reconstruction and secret sharing for general three-qubit states. This is achieved by providing a closed expression for the reconstruction fidelity, which relies on the genuine tripartite correlation and the bipartite channel between the dealer and the reconstructor characterized by the respective correlation parameters. We formulate the idea of quantum advantage in approximate state reconstruction as surpassing the classical limit set at 23\frac{2}{3}32​. This article introduces new interoperability between teleportation and state reconstruction. This is detailed through a case-by-case analysis of relevant correlation matrices. We reformulate the idea of quantum secret sharing by setting up additional constraints on the teleportation capacity of the bipartite channels between dealer and shareholders by ensuring that, individually, the shareholders cannot reconstruct the secret. We believe that this will give us an ideal picture of how quantum secret sharing should be.
The work presents a novel quantum secret sharing strategy based on GHZ product state sharing between three parties. The dealer, based on the classical information to be shared, toggles his qubit and shares the product state. The other parties make their Bell measurements and collude to reconstruct the secret. Unlike the other protocols, this protocol does not involve the entire initial state reconstruction, rather uses selective qubits to discard the redundant qubits at the time of reconstruction to decrypt the secret. The protocol also allows for security against malicious attacks by an adversary without affecting the integrity of the secret. The security of the protocol lies in the fact that each party's correct announcement of their measurement is required for reconstruction, failing which the reconstruction process is jeopardized, thereby ascertaining the (3,3)(3,3)(3,3) scheme which can further be extended for a (n,n)(n,n)(n,n) scheme.
In this paper, we propose a novel scheme for quantum two-state sharing (QTSS) by using a five-qubit entangled state as the quantum channel. In this scheme, a dealer Alice has two unknown quantum states and wants her three agents to share the quantum states. After the dealer performs a four-qubit measurement on her qubits, and the controller employs a single-qubit measurement on his own qubit, the state receivers can reconstruct the original states by using the appropriate unitary operations. It is shown that, only if all agents collaborate with each other, the QTSS can be completed with unit success probability.
Abstract In addition to secret splitting, secret reconstruction is another important component of secret sharing. In this paper, the first quantum secret reconstruction protocol is proposed to protect the reconstruction process. Before the protocol, a classical secret is divided into multiple shares that are distributed to the shareholds, respectively. In the presented protocol, the dealer utilizes the secret to encrypt a privacy quantum state, and sends the encrypted state to a combiner who is chosen by the dealer within the shareholders. With the help of other shareholders, the combiner utilizes the properties of cluster states to recover the privacy quantum state. It is shown that the proposed protocol is secure against several common attacks, including external and internal attacks. Compared with classical secret reconstruction protocols, this protocol not only achieves information‐theoretic security of all shares, but is also more efficient due to the reduced distribution and computation cost. To demonstrate the feasibility of the protocol, a corresponding simulation quantum experiment is conducted on the IBM Q. Furthermore, in conjunction with quantum fingerprinting, it can be directly applied to achieve the task of quantum multiple secrets sharing, since the classical shares can be reused in the proposed protocol.
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Quantum secret sharing is one of the most important and interesting quantum information processing task. In quantum secret sharing, information is split among several parties such that only one of them is able to recover the qubit exactly provided all the other parties agree to cooperate. To achieve this task, all the parties need to share entangled state. As far as my knowledge, all the previous quantum secret sharing protocol used either pure tripartite or pure bipartite entangled state. In this work we use for the first time bipartite two qubit mixed state (formed due to noisy environment) in quantum secret sharing scheme. We further show that one party cannot extract the information without the collaboration of other party. We also study the property of the shared mixed state used in the quantum secret sharing scheme.