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arXiv:quant-ph/9906021 · Physical Review Letters

Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network

Peter van Loock, Samuel L. Braunstein

Published Apr 10, 2000• 563 citations
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Abstract

We show that one single-mode squeezed state distributed among N parties using linear optics suffices to produce a truly N-partite entangled state for any nonzero squeezing and arbitrarily many parties. From this N-partite entangled state, via quadrature measurements of N-2 modes, bipartite entanglement between any two of the N parties can be "distilled," which enables quantum teleportation with an experimentally determinable fidelity better than could be achieved in any classical scheme.

DOI
10.1103/physrevlett.84.3482

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We show that one single-mode squeezed state distributed among N parties using linear optics suffices to produce a truly N-partite entangled state for any nonzero squeezing and arbitrarily many parties. From this N-partite entangled state, via quadrature measurements of N-2 modes, bipartite entanglement between any two of the N parties can be "distilled," which enables quantum teleportation with an experimentally determinable fidelity better than could be achieved in any classical scheme.
It is known that even a single one-mode squeezed state incident on a beamsplitter is sufficient to produce bipartite (pure-state) entanglement with respect to the field quadratures. We show that such entanglement enables quantum teleportation with a fidelity better than could be achieved in any classical scheme. Furthermore, using a continuous-variable teleportation protocol involving more than two parties, we show that a single one-mode squeezed state and linear optics is sufficient to produce a truly N-partite entangled state for arbitrarily many parties, provided that a minimal amount of squeezing is available. This multipartite entanglement may be made arbitrarily good using more and stronger one-mode squeezed states.
We present two linear optical schemes using nonideal photodetectors to demonstrate the inseparability of WWW-type NNN-partite entangled states containing only a single photon. First, we show that the pairwise entanglement of arbitrary two modes chosen from NNN optical modes can be detected using the method proposed by Nha and Kim [Phys. Rev. A 74, 012317 (2006)], thereby suggesting a full inseparability among NNN parties. In particular, this scheme is found to succeed for any nonzero quantum efficiency of photodetectors. Second, we consider a quantum teleportation network using linear optics without auxiliary modes. The conditional teleportation can be optimized by a suitable choice of the transmittance of the beam splitter in the Bell measurement. Specifically, we identify the conditions under which maximum fidelity larger than the classical bound 2/3 is achieved only in cooperation with other parties. We also investigate the case of on-off photodetectors that cannot discriminate between the number of detected photons.
First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for NNN-party continuous-variable states and discuss their applicability. Then, we consider a family of multipartite entangled states (multi-party multi-mode states with one mode per party) described by continuous quantum variables and analyze their properties. These states can be efficiently generated using squeezed light and linear optics.
In this work we point out how the continuous variable teleportation protocol takes advantage of the quadrature entanglement in different ways, depending on the preparation of the entangled state. For a given amount of the entanglement resource, we describe the best production scheme for a two-mode Gaussian state, which enables quantum teleportation with optimal fidelity. We extend this study to multiparty entangled Gaussian states and define an operative measure of multipartite entanglement related to the optimal fidelity in a quantum teleportation network experiment. This optimal fidelity is shown to be equivalent to the entanglement of formation for the standard two-user protocol, and to the multipartite localizable entanglement for the multiuser protocol.