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arXiv:1509.08438 · Quantum Information Processing

Remote preparation of W states from imperfect bipartite sources

George Moreno, Márcio M. Cunha, Fernando Parisio

Published Jun 14, 2016• 15 citations
arXivHTMLPDF
DOI
10.1007/s11128-016-1358-0

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Efficient production of WWW states from imperfect bipartite sources
Previous proposals to produce tripartite WWW-type entanglement are usually probabilistic and often based on physically unlikely events. We provide a deterministic procedure to remotely create WWW states out of an EPR source, which is easier to produce. The proposal is made viable through measurements (which can be demolitive) in an appropriate three-qubit basis and turns out to be robust against imperfections in the bipartite source. It is possible, e. g., to create a pure ensemble of WWW states out of an EPR source containing a systematic error. This simultaneously amounts to entanglement concentration and {\it lifting}.
A linear optical scheme for probabilistic remotely preparing an arbitrary bipartite entangled state is proposed. The imperfect quantum entangled channel is considered in terms of the loss and absorption of the lossy beam splitters. We investigated the influence of the loss factor on the processing of the remote state preparation. The results of numerical calculations show that the loss of beam splitters not only cut down the fidelity of the result state and remote preparation success probabilities, but also leads to unequivalent impacts on both of them when the sender chooses different orthogonal measurement basis.
The weight graph states (WGS) usually serve as the imperfect generation of the graph states due to the limitation in experiments. In this paper, we study the deterministic remote state preparation (RSP) protocol by leveraging multiple WGS. First, we introduce the quantum circuit of the entanglement concentration based on the theory of majorization, calculating the entanglement coefficients by applying the Schmidt decomposition onto the bipartite WGS. Then, we establish the positive operator-valued measurement (POVM) that helps to extract available entanglement for the RSP protocol. In three-particle 1D WGS, we demonstrate that the bipartite entanglement between the sender and the receiver depends on the measurement basis selected by the repeater node. Here we find a set of orthogonal bases that retains the entanglement unchanged, which guarantees the robustness of the RSP scheme. In the end, we discuss the performance of our protocol and extend the channel to the multi-particle 1D WGS, illustrating the relationship between the entanglements and the different weights of edges. Our scheme provides a viable method to reuse the imperfect graph states, hoping to contribute to the future study of graph states in quantum networks.