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Acta Sinica Quantum Optica

Teleportation of an Unknown Three-qubit Entangled GHZ State Under the Control of Many Supervisors in a Network

Sha Jin-Qiao

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

A scheme for teleporting an unknown three-qubit GHZ state under the control of many supervisors is presented.In order to realize the teleportation,the sender Alice needs to perform Bell state measurements on her qubit pairs and all the spatially-separated supervisors should make a Hadamard transformation and a Von Neumann measurement on their own qubit,respectively.Then the receiver Bob can restore the original state by operating some pauli matrixes with the aid of classical message from Alice and supervisors.Anyone's absence will surely fail the teleportotion.

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A scheme for teleporting an unknown three-qubit GHZ state under the control of many supervisors is presented.In order to realize the teleportation,the sender Alice needs to perform Bell state measurements on her qubit pairs and all the spatially-separated supervisors should make a Hadamard transformation and a Von Neumann measurement on their own qubit,respectively.Then the receiver Bob can restore the original state by operating some pauli matrixes with the aid of classical message from Alice and supervisors.Anyone's absence will surely fail the teleportotion.
A scheme for controlled teleportation of an unknown N -qubit entangled GHZ state from the sender Alice to the distant receiver Bob is proposed. And m -qubit GHZ state is sufficient for the task of control by m spatially-separated supervisors. Conditioned on the local operations executed by all participants, Bob can faithfully restore the original state by performing relevant unitary transformations with the aid of some classical message about measurement results. Anyone's absence will absolutely lead to the failure of teleportation.
A scheme for probabilistic controlled teleportation of a triplet W state from the sender Alice to the distant receiver Bob is proposed. In this scheme, an m -qubit GHZ state serves as the control parameter. The m control qubits are shared by m ( s 1 , s 2 . . . s m ) spatially-separated supervisors. With the aid of local operations and individual measurements, including Bell-state measurement, Von Neumann measurement, and mutual classical communication, etc., Bob can faithfully reconstruct the original state by performing relevant unitary transformations. However, even if one participant does not cooperate during the process, the receiver Bob cannot fully recover the original state. This protocol can be extended to probabilistic controlled teleportation of an arbitrary N -qubit state and some other N -qubit entangled states.
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.
A kind of three-particle entangled state is applied as quantum channel of the controlled quantum teleportation of a one-particle unknown state. The one-particle unknown state is transmitted from the sender to the recipient under the control of the supervisor. After the sender makes Bell-state measurement and the supervisor performs von Neumann measurement, the recipient carries out unitary transformation on his own particle depending on classical information from the sender and the supervisor. The teleportation cannot be completed successfully by the recipient if the supervisor does not agree to cooperate. The roles of the recipient and the supervisor may be exchanged in this scheme. The scheme is flexible and feasible because the sequence of manipulation of the sender and the supervisor may be exchanged and only simple unitary transformation is included.
It is shown that a maximally seven-qubit state can be utilized for perfect teleportation of arbitrary three qubit systems and controlled teleportation of an arbitrary three qubit state. For perfect teleportation, the sender first performs a Von-Neumann measurement on her qubits, then the sender(Alice) tells the measurement result to the receiver(Bob) via a classical channel, the receiver can reconstruct the original state by performing appropriate unitary transformations on his qubits at hand. For controlled teleportation, the sender firstly carries out proper Bell-state measurements and the controller(charlie) needs to operate a single-qubit measurement, the receiver can reconstruct the original state by applying appropriate unitary transformations on his qubits after he knows the measurement results of both the sender and controller. Besides, the two teleportation schemes can be realized with the maximal probability.
We present a scheme for perfectly teleporting an arbitrary and unknown N -particle GHZ-class state from a sender to a receiver. We just need one quantum channel composed of two or three particles in the maximally entangled state. The sender performs one Bell-state measurement on two of her particles and N −1 Hadamard operations and N −1 von Neumann measurements on the rest N −1 particles. The receiver adopts one corresponding unitary transformation on his particles shared with the sender. After that, the receiver can obtain the original N -particle GHZ-class state by introducing N −1 ancillary particles and carrying out N −1 controlled-NOT operations. We also generalize the scheme to the case of controlled teleportation.