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Journal of Modern Optics

Network controlled teleportation of N -qubit state

Wenxue Chen, Xiu-Lao Tian, Ming‐Liang Hu

Published Sep 27, 2010• 7 citations
Publisher

Abstract

By employing the tensor analysis technique, we propose three schemes of controlled teleportation: series controlled, circular controlled and network controlled teleportation. We discuss the necessary and sufficient condition for realizing these schemes, in which we use a general two-qubit entangled state instead of the GHZ state as the communication channel. This enables successful implementation of teleportation without using the Hadamard operation.

DOI
10.1080/09500340.2010.514075

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By employing the tensor analysis technique, we propose three schemes of controlled teleportation: series controlled, circular controlled and network controlled teleportation. We discuss the necessary and sufficient condition for realizing these schemes, in which we use a general two-qubit entangled state instead of the GHZ state as the communication channel. This enables successful implementation of teleportation without using the Hadamard operation.
According to the collapse principle of quantum state when being measured, we present a method of directly writing out transformation matrix by looking at the figure of a network-controlled quantum channel. We find the rule of constructing transformation matrix in network-controlled teleportation. Based on this method, we gain transformation matrix of two-qubit state teleportation in which two GHZ state act as controlled quantum channels. We further proposed a scheme of one-qubit teleportation by a series-controlled quantum channel and teleportation of three-qubit via a typical network controlled quantum channel, in which two-qubit state instead of GHZ state act as quantum channel. So, Hadamard operation is not necessary in our scheme.
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.
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.
We study the general case of controlled quantum teleportation and give analytic expressions for the maximal probabilities of successful controlled teleportation of an unknown qubit via every kind of three-qubit state. We also give an explicit expression for the three-qubit states that can be used as quantum channel for controlled teleportation of an unknown state with unit probability and with unit fidelity. In addition, an exact value of localizable entanglement is determined. We obtain the necessary and sufficient condition that a three-qubit state can be collapsed to an EPR pair by a measurement on one qubit.
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.
We put forward an efficient quantum controlled teleportation scheme, in which arbitrary two-qubit state is transmitted from the sender to the remote receiver via two entangled states under the control of the supervisor. In this paper, we use the combination of one two-qubit entangled state and one three-qubit entangled state as quantum channel for achieving the transmission of unknown quantum states. We present the concrete implementation processes of this scheme. Furthermore, we calculate the successful probability and the amount of classical information of our protocol.