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Chinese Physics Letters

Probabilistic Controlled Teleportation of a Triplet W State

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

Published May 1, 2007• 20 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/24/5/005

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Acta Sinica Quantum Optica•Jan 1, 2007•0 citations
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.
A scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of two Einstein–Podolsky–Rosen (EPR) states and one Greenberger–Horne–Zeilinger (GHZ) state is proposed. In this scheme, an (m + 2 )-qubit GHZ state serves not only as the control parameter but also as the quantum channel. The m control qubits are shared by m 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. The total probability of successful teleportation is only dependent on channel coefficients of EPR states and GHZ, independent of the number of supervisor m. This protocol can also be extended to probabilistic controlled teleportation of an arbitrary N-qubit state using combined non-maximally entangled channel of N – 1 EPR states and one (m + 2 )-qubit GHZ.
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 is presented to probabilistically controlled teleport an arbitrary triplet W state using three pair maximally entangled triplet W state as the quantum channel. During the teleportation procedure, the controller performs Von Neumann measurements on his particles, the sender makes orthogonal basis measurements, instead of using Bell-state measurements, and the receiver can faithfully reconstruct the original state by performing relevant unitary transformations. The total probability of successful teleportation can be improved to 20/27. unitary transformation
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-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.