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Physics Letters A

Perfect teleportation of arbitrary n-qudit states using different quantum channels

Zhanjun Zhang, Yimin Liu, Dong Wang

Published Jul 14, 2007• 78 citations
Publisher
DOI
10.1016/j.physleta.2007.07.017

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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.
In this paper, we study the teleportation of arbitrary N-qudit state with the tensor representation. The necessary and sufficient condition for realizing a successful or perfect teleportation is obtained, as will be shown, which is determined by the measurement matrix Tδ and the quantum channel parameter matrix X. The general expressions of the measurement matrix Tδ are written out and the quantum channel parameter matrix X are discussed. As an example, we show the details of three-ququart state teleportation.
In this study,we will investigate the problem of teleportation of an arbitrary two-qubit state.Firstly,we show how the two-qubit state can be teleported with unit fidelity and unit probability by using a maximally entangled four-dimensional qudit pair as a quantum channel.Then,we put forward a scheme for probabilistic teleporting the state with unit fidelity via a partially entangled quantum qudit channel.The probability of successful teleportation is determined by the smallest Schmidt coefficient of the entangled qudit pair.