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arXiv:quant-ph/9906075 · Physical Review A

Unconditional teleportation of continuous-variable entanglement

Peter van Loock, Samuel L. Braunstein

Published Dec 8, 1999• 149 citations
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Abstract

We give a protocol and criteria for demonstrating unconditional teleportation of continuous-variable entanglement (i.e., entanglement swapping). The initial entangled states are produced with squeezed light and linear optics. We show that any nonzero entanglement (any nonzero squeezing) in both of two entanglement sources is sufficient for entanglement swapping to occur. In fact, realization of continuous-variable entanglement swapping is possible using only two single-mode squeezed states.

DOI
10.1103/physreva.61.010302

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We give a protocol and criteria for demonstrating unconditional teleportation of continuous-variable entanglement (i.e., entanglement swapping). The initial entangled states are produced with squeezed light and linear optics. We show that any nonzero entanglement (any nonzero squeezing) in both of two entanglement sources is sufficient for entanglement swapping to occur. In fact, realization of continuous-variable entanglement swapping is possible using only two single-mode squeezed states.
A pair of entangled states of light with classical coherence and independent quantum fluctuations has been produced from two home-designed and home-made non-degenerate optical parametric amplifiers. Utilizing these entangled states we have experimentally demonstrated unconditional entanglement swapping for continuous variables, i.e. quantum teleportation of an entangled state. Based on the direct detection of Bell states and entanglement collapse, two optical beams which have never directly interacted with each other are entangled together. The degrees of quantum correlation resulting from the entanglement swapping have been determined by direct measurement to be 1.23dB and 1.12dB below the shot noise limit for the amplitude and phase quadratures, respectively. The theoretical calculation and experimental measurements are in reasonable agreement.
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 a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.