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arXiv:0706.0098 · Chinese Physics Letters

Controlled Teleportation of an Arbitrary Multi-Qudit State in a General Form with d -Dimensional Greenberger–Horne–Zeilinger States

Xihan Li, Deng Fu-Guo, Hong-Yu Zhou

Published May 1, 2007• 93 citations
arXivHTMLPDF

Abstract

A general scheme for controlled teleportation of an arbitrary multi-qudit state with d -dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m -qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2 m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m -qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.

DOI
10.1088/0256-307x/24/5/007

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A general scheme for controlled teleportation of an arbitrary multi-qudit state with d -dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m -qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2 m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m -qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.
A scheme for generalized controlled teleportation of an arbitrary two-quNit entangled state with N -dimensional partially Greenberger–Horne–Zeilinger (GHZ) state is proposed. A generalized Bell state measurement (BM) and a single-particle measurement in high dimensions are needed. According to the sender Alice's classical message, the receiver Charlie can restore the unknown two-quNit state with a certain probability by introducing an additional particle and performing a controlled-not (C-NOT) operation on his particles if she cooperates with the controller Bob. The total success probability and classical communication cost are calculated. We also generalize the scheme to the case where there are K controllers. It is shown that any one of the receivers can reconstruct the unknown state if he/she cooperates with all the controllers.
We present a general scheme for multiparty-controlled teleportation of an arbitrary m -qudit ( d -dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2 m particles, the controllers take some single-particle measurements with the measuring basis X d and the receiver only needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m -qudit state equals the entanglement of the quantum channel.
We present a general scheme for multiparty-controlled teleportation of an arbitrary m-qudit (ddd-dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2mmm particles, the controllers take some single-particle measurements with the measuring basis XdX_{d}Xd​ and the receiver only need to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid some a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m-qudit state equals to the entanglement of the quantum channel.
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 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.
We present a scheme for symmetric multiparty quantum state sharing of an arbitrary m -qubit state with m Greenberger–Horne–Zeilinger states following some ideas from the controlled teleportation (2005 Phys. Rev. A 72 02338). The sender Alice performs m Bell-state measurements on her 2 m particles and the controllers need only take some single-photon product measurements on their photons independently, not multipartite entanglement measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown m -qubit state and it is an optimal one as its efficiency for qubits approaches 100% in principle.