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Journal of Foshan University

Teleportation of an arbitrary two-qubit state via an entangled four-dimensional qudit pair channel

Yi-Hong Bai

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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.

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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.
A scheme for teleporting an unknown quantum state via a partially entangled particle pair is proposed. We show that teleportation can be successful realized with unit fidelity but less than unit probability if the sender performs a rotational operation on the teleported qubit and then performs computation basis measurements on the teleported particle and the half of the entangled particle pair respectively. The probability of successful teleportation is determined by both Schmidt coefficients of the entangled pair. This method can be generalized to the teleportation of an arbitrary and unknown multi-qubit state.
We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation.
Teleportation of an arbitrary single-qubit state using two partially entangled states is considered.Firstly,we present a method for realizing probabilistically two-destination teleportation by using two partially entangled pairs as quantum channel.Then,we put forward a scheme for realizing deterministic and exact teleportation by using same quantum channel.In these schemes,the sender's local generalized measurement described by a positive operator valued measurement(POVM) lies at the heart.We construct the required POVM.The methods are applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are 2μ+2μv-2v-1≥0.
Two schemes for teleporting an unknown two-particle entangled state via a four-qubit non-maximally entangled cluster state as quantum channel are proposed.In the first scheme,a special bipartite entangled state was teleported,the receiver Bob can reconstruct the original state with a certain probability according to the sender Alice's measurement results,and the successful probability is determined by the smallest two coefficients' absolute values of the cluster state.In the latter scheme an arbitrary two-particle entangled state was teleported.Contrast to the first scheme, Bob should perform a quantum controlled phase gate operation besides the unitary transformation. The considerable advantage is that it employs a non-maximally entangled cluster state as quantum channel in these two schemes.Thus,the schemes can greatly reduce the amount of entanglement resources and need less classical bits.
Abstract Based on the four-qubit cluster state as quantum channel, we put forward a novel scheme for teleporting a two-qubit arbitrary entangled state. The necessary quantum operations for accomplishing the task are two controlled-not gate operations, one controlled-phase gate operation, four single-qubit measurements and two single-qubit transformed operations. They are easily achievable with current experimental techniques. Besides, the present scheme is deterministic because its probability of success is 100 % .