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International Journal of Quantum Information

A GENERAL METHOD TO FIND PROPER CHANNEL FOR THREE-QUBIT STATE TELEPORTATION

Xiu-Lao Tian, Xiao-Qiang Xi

Published Aug 1, 2009• 6 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749909005535

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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.
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, 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.
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.
A scheme of teleportation of an arbitrary three-qubit state is presented by using the generalized Bell-basis measurement and the Non-Bell-Pair quantum channel.Teleportation can be perfectly realized if Alice makes Bell-state measurement on her particles and Bob carries out appropriate unitary transformation(Toffoli transformation)on his particle.The unknown three-particle entangled state can be teleported perfectly,and the successful possibilities and fidelities of the two schemes both reach unity.Based on the transformation operator,the collapses states can easily obtained and Bob's unitary transformation can also easily given.
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.