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Quantum Information Processing

Quantum teleportation with partially entangled states via noisy channels

Hua-Qiu Liang, Jin‐Ming Liu, Shangshen Feng, Ji-Gen Chen

Published Mar 6, 2013• 20 citations
Publisher
DOI
10.1007/s11128-013-0555-3

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Partial teleportation of entanglement is to teleport one particle of an entangled pair through a quantum channel. This is conceptually equivalent to quantum swapping. We consider the partial teleportation of entanglement in the noisy environment, employing the Werner-state representation of the noisy channel for the simplicity of calculation. To have the insight of the many-body teleportation, we introduce the measure of correlation information and study the transfer of the correlation information and entanglement. We find that the fidelity becomes smaller as the initial state is entangled more for a given entanglement of the quantum channel. The entangled channel transfers at least some of the entanglement to the final state.
Transfer of entanglement and information is studied for quantum teleportation of an unknown entangled state through noisy quantum channels. We find that the quantum entanglement of the unknown state can be lost during the teleportation even when the channel is quantum correlated. We introduce a fundamental parameter of correlation information which dissipates linearly during the teleportation through the noisy channel. Analyzing the transfer of correlation information, we show that the purity of the initial state is important in determining the entanglement of the replica 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.