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Modern Physics Letters A

Quantum state sharing of an arbitrarym-particle state using Einstein–Podolsky–Rosen pairs and application in quantum voting

Comfort Sekga, Mhlambululi Mafu

Published Jul 10, 2021• 5 citations
Publisher

Abstract

In this paper, we propose a scheme where Alice shares an arbitrary m-particle unknown state with her agents, Bob and Charlie. Alice starts by distributing 2m Einstein–Podolsky–Rosen pairs with her agents and performs m joint three-particle Greenberger–Horne–Zeilinger state measurements on her particles. Bob, who acts as the controller, performs a product measurement [Formula: see text] on his m qubit states while Charlie retrieves the original state by performing unitary operations on his m particles. Subsequently, we demonstrate our proposed scheme’s feasibility by applying it in electronic voting by sharing an arbitrary single-particle state.

DOI
10.1142/s0217732321501510

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A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the NNN agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers. Moreover, each of the controllers is required to take only a product measurement ${\ensuremath{\sigma}}_{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{x}$ on his two particles, which makes this scheme more convenient for the agents in the applications on a network than others. As all the quantum source can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. With a new notation for the multipartite entanglement, the sender need only publish two bits of classical information for each measurement, which reduces the information exchanged largely.
A scheme to teleport an unknown two qubit state from Alice (the sender) to Bob (the receiver) using two Einstein Podolsky Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.
We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n − 1 auxiliary particles in the initial state |0⟩, applies Hadamard (H) gate and Controlled-Not (CNOT) gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers (i.e., other n − 1 agents), where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.
We present a scheme for symmetric multiparty quantum state sharing of an arbitrary m -qubit state with m Greenberger–Horne–Zeilinger states following some ideas from the controlled teleportation (2005 Phys. Rev. A 72 02338). The sender Alice performs m Bell-state measurements on her 2 m particles and the controllers need only take some single-photon product measurements on their photons independently, not multipartite entanglement measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown m -qubit state and it is an optimal one as its efficiency for qubits approaches 100% in principle.
A rational quantum state sharing protocol with the semi-off-line dealer is proposed. Firstly, the dealer Alice shares an arbitrary two-particle entangled state with the players by Einstein–Podolsky–Rosen (EPR) pairs and Greenberger–Horne–Zeilinger (GHZ) states. The EPR pairs are prepared by Charlie instead of the dealer, reducing the workload of the dealer. Secondly, all players have the same probability of reconstructing the quantum state, guaranteeing the fairness of the protocol. In addition, the dealer is semi-off-line, which considerably reduces the information exchanging between the dealer and the players. Finally, our protocol achieves security, fairness, correctness, and strict Nash equilibrium.
Focused on the issue that the quantum secret sharing is limited to the maximally entangled state,a scheme for quantum state sharing of an arbitrary unknown N-qubit state by using entangled state as quantum channel was proposed. The sender Alice used the Bell basis measurement and then the receiver Bob or Charlie used the single particle measurement. The participants chose the right joint unitary operation according to the results from Alice and the signal measurement,which could realize arbitrary N-qubit secret sharing. The eavesdropping analysis shows explicitly that the scheme is secure and it can resist the external eavesdropper and internal dishonest participant.