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Spatially distributed multipartite entanglement enables EPR steering of atomic clouds

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Science  27 Apr 2018:
Vol. 360, Issue 6387, pp. 413-416
DOI: 10.1126/science.aao2254
  • Fig. 1 Distribution of entanglement.

    In a tightly trapped BEC, entanglement in the spin degree of freedom is generated by local spin-mixing interactions. Switching off the longitudinal confinement leads to a rapid expansion of the atomic cloud, which distributes the entanglement spatially. After local spin measurements with high spatial resolution, we partitioned the detected atomic signal into distinct subsystems. We demonstrated EPR steering between these parts, which evinces the presence of bipartite and even multipartite entanglement.

  • Fig. 2 EPR steering.

    (A) A global change of the phase ϕ before the measurement allows mapping of the spin observable Embedded Image to the read-out direction Embedded Image (inset). We partitioned the atomic signal into two halves and observed that for subsystem A, the fluctuations of Embedded Image are, depending on the value of phase ϕ, reduced or enhanced compared with the shot-noise limit of a fully separable spin state (dashed line). The solid line is a theoretical prediction based on our experimental parameters (27). At phase ϕ = 0, fluctuations are reduced, whereas the fluctuations are enhanced at phase ϕ = π/2. (B) The measurement result in subsystem B is used to infer the result in subsystem A (inset), leading to an inference variance Embedded Image. The solid line represents the theoretical prediction. The data in the gray shaded region are used to calculate the EPR steering product SA|B. (C) We varied the spatial separation (d) between the two subsystems by discarding a fraction η of atomic signal in the middle of the cloud (inset). The red and blue diamonds are the products Embedded Image of the inference variances after 60 and 150 ms of spin-mixing time (tevo), respectively. The individual inference variances Embedded Image at ϕ = 0 and ϕ = π/2 are shown as black triangles and squares, respectively. The steering product remains below the EPR steering bound even if a substantial fraction of the atomic signal is discarded, confirming the spatial distribution of entanglement in our system. The error bars correspond to an estimation of the 1-SD interval.

  • Fig. 3 Three-way EPR steering.

    By partitioning the absorption signal into three parts of equal length (~20 μm), we show that each of the three subsystems is steered by the other two. For each case, we calculate the steering product Embedded Image, where Embedded Image denotes the optimal inference on the observable Embedded Image in subsystem α, using the information obtained from the other two subsystems (β, γ). The red (blue) points are the results for 60 ms (150 ms) of spin-mixing time. The black line represents the steering bound. The error bars correspond to an estimation of the 1-SD interval.

  • Fig. 4 Genuine multipartite entanglement.

    In the bipartite steering scenario, the possible inference of subsystem B on subsystem A is used to reveal genuine multipartite entanglement. For each partition A|B, quantified by ηA = NA/N, subsystem B can be divided into additional m – 1 parts of equal atom number (the inset shows an example). The regions where genuine m-partite entanglement is witnessed according to Eq. 5 are indicated by the blue shadings, where the corresponding m is given on the right. The upper (lower) panel shows the results for 60 ms (150 ms) of spin-mixing time. The lowest bound is given by the Heisenberg uncertainty limit for our observables in the full system. The error bars correspond to an estimation of the 1-SD interval.

Supplementary Materials

  • Spatially distributed multipartite entanglement enables EPR steering of atomic clouds

    Philipp Kunkel, Maximilian Prüfer, Helmut Strobel, Daniel Linnemann, Anika Frölian, Thomas Gasenzer, Martin Gärttner, Markus K. Oberthaler

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S8
    • References
    Data S1

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