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Communications in Theoretical Physics

Teleportation of N -Particle Entangled GHZ State via Entanglement Swapping

Sha Jin-Qiao, Fang Jian-Xing, Zhu Shi-Qun, Jiang Wei-Xing, Xuemin Qian

Published Oct 1, 2006• 1 citation
Publisher

Abstract

In this scheme, N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N -particle entangled GHZ state via entanglement swapping. In order to realize this teleportation, the sender Alice operates Bell-state measurement on particles belonging to herself. Then she informs the results to the receiver Bob through classical communication. According to the results, Bob operates corresponding transformation to reconstruct the initial state. The advantage of this scheme is that it needs only one common unitary matrix for Alice's different results, which has a more general meaning. As a special case, teleporting an unknown three-particle entangled GHZ state is proposed.

DOI
10.1088/0253-6102/46/4/005

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In this scheme, N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N -particle entangled GHZ state via entanglement swapping. In order to realize this teleportation, the sender Alice operates Bell-state measurement on particles belonging to herself. Then she informs the results to the receiver Bob through classical communication. According to the results, Bob operates corresponding transformation to reconstruct the initial state. The advantage of this scheme is that it needs only one common unitary matrix for Alice's different results, which has a more general meaning. As a special case, teleporting an unknown three-particle entangled GHZ state is proposed.
In this scheme, N pairs of non-maximally entangled particle are used as quantum channel to teleport an unknown N-particle entangled W state via entanglement swapping, which has more generality. In order to realize this teleportation, the sender Alice performs Bell-measurements on particles belonging to her. Then the sender sends the results to the receiver Bob through the classical channel. According to the results, Bob performs a corresponding unitary on particles to reconstruct the original state. And then, teleporting an unknown three-particle entangled W state is presented.
In this paper, quantum teleportation of one-to-many using ( n +1)-particle entanglement is presented. If the sender (Alice) wants to transmit an unknown quantum state to a distant receiver (Bob), similar to the previous schemes, Alice performs Bell-state measurement on particles belonging to herself and informs the receiver the results through the classical channel. After that, it needs to perform the Hadamard operation on the other ( n −1) particles and measure them as well. With the aid of the measurement results, Bob can operate a corresponding unitary transformation on his particle to reconstruct the original state. Of course, the reconstruction may realize at either location of n , but it cannot realize at all locations at the same time.
Recently, there is much interest in the study of quantum teleportation. Its marvelous security property makes it particularly attractive as potential means for future communication. Uncertain principal and no-cloning theories of quantum mechanics forbid exact copy of quantum states. To solve the problem, quantum teleportation devides message state into two parts: classical message and quantum message which are transmitted through relevant classical and quantum channels from a sender Alice to a distant receiver Bob, respectively. According to both message states, Bob can recover the original message state with certain possibility. Utilizing the general quantum teleportation protocol, in this scheme, a new method is presented by which multi-qubit quantum information can be teleported in a much easier way. It has been extended to teleportation of an arbitrary N-qubit state via entanglement swapping and probabilistic teleportation is investigated as well, which has a more general meaning. N non-maximally entangled triplet GHZ states (Greenberger-Home-Zeilinger), taking the place of the previous EPR states (Einstein-Podolsky-Rosen), serve as quantum channels, which avoids introducing extra auxiliary qubit. In order to complete the teleportation, Alice has to devide all qubits into N parts and make Bell-State measurement on qubit pair (i, x(subscript i)) and tell Bob the measurement result through classical channel, then Bob perform some simple local operations on qubits (y(subscript i), z(subscript i)) to finish teleporting the i-th qubit. Conditioned on N-times similar repeat, Bob can faithfully reconstruct the initial state. Results show that, in this method, the identification difficulty of entangled states is considerably reduced, the new method is more feasible in technique. And the total possibility of successful teleportation is (The equation is abbreviated). As a special case, teleportation of an arbitrary two-qubit state is proposed.
A scheme for teleporting an unknown three-particle GHZ state from a sender to either one of two receivers is proposed. In this scheme, the quantum channel is composed of two non-maximally three-particle entangled W states. An unknown three-particle GHZ state can be perfectly teleported probabilistically if the sender performs two generalized Bell-state measurements and the Hadamard operation while either one of two receivers introduces an ancillary particle which is one of the final three particle constituting the teleported state, then performs the controlled-not operation with the ancillary particle as the target bit and introduces an appropriate unitary transformation with the help of the other receiver's simple measurements. All kinds of unitary transformations are given in detail. The present scheme may be directly generalized to teleport an unknown multiparticle GHZ state via two three-particle entangled W states used as the quantum channel.
A scheme for teleporting an unknown three-particle GHZ state from a sender to either one of two receivers through a non-maximally three-particle entangled GHZ state as quantum channel is proposed.An unknown three-particle entangled state can be perfectly teleported probabilistically if the sender performs a generalized Bell-state measurement and the Hadamard operations while either one of two receivers introduces two additional particles,performs the controlled-not(C-not) operations and introduces an appropriate unitary transformation with the help of the other receiver's the Hadamard operation and simple measurement.The present scheme may be directly generalized to teleport an unknown k-particle GHZ state from a sender to either one of two receivers by using a partial entangled three-particle GHZ state as the quantum channel,introducing(k-1) additional qubits and performing(k-1) C-not operations.