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Journal of Modern Optics

A general method of controlled bidirectional quantum teleportation of qudit state

Cong Liao, Simeng Wang, Caifang Wang, Hua-Bo Liu, Xiu-Lao Tian

Published Mar 23, 2017• 4 citations
Publisher

Abstract

Based on tensor representation and d-dimensional Bell basis measurements, we obtained a necessary condition for realizing controlled bidirectional quantum teleportation of qudit states. To verify its theoretical feasibility, we further give a general and simple method of selecting quantum channels for teleporting the ququart state.
DOI
10.1080/09500340.2017.1296596

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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.
Qudit quantum system can carry more information than that of qubit,so it is an important resource in quantum information processing.The ququart state with the tensor representation is gotten in term of the photon entangled state.The necessary and sufficient condition for realizing a successful or perfect teleportation is obtained,as will be shown,this condition is determined by the measurement matrix and the quantum channel parameter matrix.The general expressions of the measurement matrix are written out and the quantum channel parameter matrix are discussed.Furthermore,the teleportation of ququart state is proposed via different kinds of quantum channels.The description of the teleporting process with the help of tensor analysis is more compact and clear.
In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented.
Qudit quantum system can carry more information than that of qubit, the teleportation of qudit state has significance in quantum information task. We propose a method to teleport a general qutrit state (three-level state) and discuss the necessary and sufficient condition for realizing a successful and perfect teleportation, which is determined by the measurement matrix Tα and the quantum channel parameter matrix (CPM) X. By using this method, we study the channels of two-qutrit state and three-qutrit state teleportation.
Based on tensor analysis and Bell basis measurement, we propose a general method to find proper channel for successful teleportation of an unknown three-qubit state. Instead of starting from "the proper channel" as that of the previous work, we begin from the successful teleportation then trace back to find which channel is proper and why it is proper for successful teleportation. At last, we give the necessary and sufficient condition for three-qubit perfect teleportation. This condition can guide us to design the corresponding channel for realizing the teleportation. Furthermore, the description of teleporting process with the help of tensor analysis is more compact and clear. Our method can also be generalized to find the channel for N-qubit successful teleportation.