Revocation and Reconstruction of Shared Quantum States

TL;DR

This paper explores methods for revoking shared quantum states using entangled resources, ensuring control over state reconstruction even with dishonest participants, and introduces protocols with specific four-qubit states.

Contribution

It proposes a novel quantum state revocation protocol utilizing four-qubit entangled states, enhancing control and security in quantum sharing schemes.

Findings

Successful revocation depends on classical outcomes during sharing.

The protocol's effectiveness varies with parameters of the four-qubit entangled states.

It provides a range of states where the protocol guarantees success.

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.