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International Journal of Quantum Information

TELEPORTATION OF N-QUDIT STATE

JIA-JIA SHAO, Xiu-Lao Tian, Guo-Fang Shi

Published Feb 1, 2012• 3 citations
Publisher

Abstract

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.

DOI
10.1142/s021974991250013x

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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.
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.
We propose a method to realize the teleportation of an unknown entangled state that consists of many qudits through a partially entangled-qudit quantum channel with the help of 2log 2 d -bit classical communication. The operations used in the teleportation process include a generalized Bell-state measurement and a series of single-qudit π-measurements performed by Alice, a series of generalized qudit-Pauli gates and two-level unitary gates, as well as a qubit measurement performed by Bob. For a maximally entangled quantum channel, the successful probability of the teleportation becomes unit.
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.