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International Journal of Modern Physics C

MULTIPARTY QUANTUM STATE SHARING OF m-QUBIT STATE

Li Dong, Xiao‐Ming Xiu, Yajun Gao

Published Nov 1, 2007• 12 citations
Publisher

Abstract

A scheme for quantum state sharing (QSTS) of a one-particle state is proposed for a three-particle GHZ state utilized as a quantum channel. After the sender (Alice) makes Bell-state measurements (BM) on her particles, and the controller (Charlie) performs a computational basis measurement (CM), the recipient (Bob) only needs to carry out a unitary transformation of the classical information from the sender and the controller. Finally, the scheme is generalized to multiparty QSTS of a one-qubit state with n agents and an m-qubit state with n agents.

DOI
10.1142/s0129183107011674

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A scheme for quantum state sharing (QSTS) of a one-particle state is proposed for a three-particle GHZ state utilized as a quantum channel. After the sender (Alice) makes Bell-state measurements (BM) on her particles, and the controller (Charlie) performs a computational basis measurement (CM), the recipient (Bob) only needs to carry out a unitary transformation of the classical information from the sender and the controller. Finally, the scheme is generalized to multiparty QSTS of a one-qubit state with n agents and an m-qubit state with n agents.
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.
Two schemes of teleporting an N-particle arbitrary and unknown state are proposed when N groups of three-particle general W states are utilized as quantum channels. In the first scheme, the quantum channels are shared by the sender and the recipient. After the sender's Bell-state measurements on his (her) particles, the recipient carries out unitary transformations on his (her) particles. And then, the recipient performs computational basis measurements to realize the teleportation. The recipient can recover the state on either of particle sequences with the equal maximal probability of successful teleportation if he (she) performs appropriate unitary transformations. In the second scheme, the quantum channels are shared by the sender, the recipient and the third ones. After the sender's Bell-state measurements and the third ones' computational basis measurements if they agree to cooperate, the recipient will introduce auxiliary particles and carry out appropriate unitary transformations. Finally, the recipient performs computational basis measurements to fulfill the teleportation. The second scheme can be realized if and only if the third ones agree to cooperate with the recipient.
In this paper, we propose a controlled quantum state sharing scheme to share an arbitrary two-qubit state using a five-qubit cluster state and the Bell state measurement. In this scheme, the five-qubit cluster state is shared by a sender (Alice), a controller (Charlie), and a receiver (Bob), and the sender only needs to perform the Bell-state measurements on her particles during the quantum state sharing process, the controller performs a single-qubit projective measurement on his particles, then the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his particles after he has known the measured results of the sender and the controller.
Abstract In this paper, we present a novel scheme for cyclic quantum state sharing (QSTS) by using a nine-qubit entangled state as quantum channel. In this scheme, each of the three dealers has a different unknown quantum state, and every dealer wants two agents to share his/her quantum state. At the same time, three dealers perform Bell basis measurements on his/her own qubits, and the controllers make a single-qubit measurement on his/her own qubits, after that, the receivers can recover the original states by applying suitable unitary operations, respectively. It is shown that, only if all agents collaborate with each other, the cyclic QSTS can be completed with unit success probability.
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.
Quantum information splitting(QIS) or quantum state sharing is the generalization of classical secret sharing schemes to the quantum scenario.In QIS,a piece of quantum information(in the form of a quantum state) is divided and distributed to a number of receivers.A scheme of splitting two-qubit states was proposed by using six-particle maximally entangled state as the quantum channel.Alice first performs two Bell-basis measurement and announces her measurement outcome and assigns Charlie(Bob) to reconstruct the original unknown state.If the controllers Bob(Charlie) agree to help Charlie(Bob) obtain the original state,they should perform single-particle measurements on their respective qubits.After the sender performs Bell-basis measurements on her particles,and the cooperators operate single-particle measurements on their particles,the state receiver can reconstruct the original state of the sender by applying the appropriate unitary operation.