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arXiv:1210.2201

Quantum Teleportation within a Quantum Network

Hari Prakash, Ajay K Maurya, Mishra, Manoj K

Published Oct 8, 2012• 0 citations
arXivHTMLPDF

Abstract

We consider the problem of teleporting an unknown information state within a quantum network by a sender, say, Alice to any given receiver out of several receivers, say, Bob(1), Bob(2), ...., Bob(n). For this task, we suggest two schemes using (n+1)-partite GHZ state as a quantum channel. The first scheme involves C-NOT operations on qubit of Bobs with the control as qubit of Alice, while the second scheme involves measurements in the Hadamard basis by Bobs on their qubits. We have generalized both schemes for quantum teleportation of arbitrary m-qubit information state within the quantum network. Further, we have proposed two experimental schemes for the generation of (n+1)-partite GHZ state using interaction between highly detuned Λ-type three-level atoms and optical coherent field. We also discuss the possible experimental imperfections like, atomic-radiative time, cavity damping time and atom-cavity interaction time.

DOI
10.48550/arxiv.1210.2201

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We consider the problem of teleporting an unknown information state within a quantum network by a sender, say, Alice to any given receiver out of several receivers, say, Bob(1), Bob(2), ...., Bob(n). For this task, we suggest two schemes using (n+1)-partite GHZ state as a quantum channel. The first scheme involves C-NOT operations on qubit of Bobs with the control as qubit of Alice, while the second scheme involves measurements in the Hadamard basis by Bobs on their qubits. We have generalized both schemes for quantum teleportation of arbitrary m-qubit information state within the quantum network. Further, we have proposed two experimental schemes for the generation of (n+1)-partite GHZ state using interaction between highly detuned Λ-type three-level atoms and optical coherent field. We also discuss the possible experimental imperfections like, atomic-radiative time, cavity damping time and atom-cavity interaction time.
In the past decades, various schemes of teleportation of quantum states through different types of quantum channels (a prior shared entangled state between the sender and the receiver), e.g. EPR pairs, generalized Bell states, qubit GHZ states, standard W states and its variations, genuine multiqubit entanglement states, etc., have been developed. Recently, three-qutrit quantum states and two-qudit quantum states have also been considered as quantum channels for teleportation. In this paper, we investigate the teleportation of an unknown qudit using a d level GHZ state, i.e. a three-qudit maximally entangled state, as quantum channel. We design a general scheme of faithful teleportation of an unknown qudit using a d-level GHZ state shared between the sender and the receiver, or among the sender, the receiver and the controller; an unknown two-qudit of Schmidt form using a d level GHZ state shared between the sender and the receiver; as well as an unknown arbitrary two-qudit using two shared d level GHZ states between the sender, the receiver and the controller, or using one shared d level GHZ state and one shared generalized Bell state. We obtain the general formulas of Alice's measurement basis, Charlie's measurement basis and Bob's unitary operations to recover the input state of Alice. It is intuitionistic to generalize the protocols of teleporting an arbitrary two-qudit state to teleporting an arbitrary n-qudit state.
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 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 of two-way teleportation was proposed,with GHZ quadripartite entangled state as quantum channel.Two sides of communication(Alice and Bob) shared two pairs of GHZ quadripartite entangled state in advance.After communication,Alice and Bob performed quantum projection measurement on their own qubits respectively,and announced the measured results via classical channel.Then according to the measured results presented by the other party,Alice and Bob can make appropriate unitary transformations that its own party can reconstruct the opposite quantum state information,and thus the whole two-way teleportation was realized.As long as the both sides of communication chose the suitable GHZ entangled state as quantum channel and distributed the entangled partites imparity and properly in advance,two-way teleporting including unknown general one qubit and two qubits entangled Bell state or three qubits entangled GHZ state could be realized respectively.
A multiparty-controlled teleportation (M-CT) scheme for securely teleporting an arbitrary unknown single-qubit state by using generalised Greenberger-Horne-Zeilinger (GHZ) states is presented in this paper, i.e., a sender, Alice, transmits an arbitrary single-qubit state to a distant receiver, Bob, under approving by all N controllers Charliei(i = 1, 2, …, N) in a quantum communication network. It is proved feasibly and easily to realise by quantum entanglement. The security of proposed scheme is also discussed. We make sure of the security of the quantum channel between the parties by decoy states. This scheme also can be used to share a quantum secret information in quantum secret sharing.
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.