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On-demand photonic entanglement synthesizer

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Science Advances  17 May 2019:
Vol. 5, no. 5, eaaw4530
DOI: 10.1126/sciadv.aaw4530

Figures

  • Fig. 1 Various types of entanglement.

    (A) Types of entanglement that can be generated by our entanglement synthesizer. (B) Types of entanglement that are actually generated and verified in this experiment. Orange spheres represent quantum modes. Blue arrows connecting two modes mean that the connected nodes can communicate with each other by use of the entanglement. Brown links connecting two modes mean that an entangling gate to generate cluster states is applied between these modes.

  • Fig. 2 Schematic of an on-demand entanglement synthesizer.

    (A) Conceptual schematic. (B) Time sequence for changing system parameters. (C) Equivalent circuit. (D) Experimental setup. See Materials and Methods for details. “H” and “V” denote horizontal and vertical polarization, respectively. OPO, optical parametric oscillator; PBS, polarizing beam splitter; QWP, quarter wave plate; EOM, electro-optic modulator; LO, local oscillator. (E) Actual control of beam splitter transmissivity T(t). Both measured (blue line) and ideal (black dotted line) responses are plotted.

  • Fig. 3 Generation of a one-dimensional cluster state.

    (A) Schematic. (B) Single-shot measurement of quadratures for the first 15 modes. x^k (p^k) is measured for odd (even) number modes and plotted as red squares (blue circles). (C) Comparison between p^k (blue circles) and x^k1+x^k+1 (red diamonds). (D) Measured variance of nullifier δ^k2 for (i) vacuum states (as a reference; black dots) and (ii) cluster states (blue dots). The SE of each variance is around 0.01 and always below 0.03. The yellow shaded area represents the inseparable region.

  • Fig. 4 Storage of one part of an EPR state in the loop.

    (A) Control sequence. (B) Measured inseparability parameter [Δ(x̂1x̂2)]2+[Δ(p̂1+p̂2)]2 with SE is plotted for each delay nτ (τ = 66 ns, n = 1, 2, …, 11). The yellow shaded area represents the inseparable region.

Tables

  • Table 1 Control sequence and inseparability parameters for various entangled states.

    T(t) and θ(t) are controlled by the sequence in Fig. 2B with the setting values (T1, T2, … ) and (θ1, θ2, … ) defined in this table. φ(t) is also controlled to measure the inseparability parameter for each state. The generated state is inseparable when each inseparability parameter is below 1 (ℏ = 1/2). The expression of inseparability parameters is given in (11, 14, 20, 21).

    Type of entanglement(T1, T2, … )1, θ2, … )Inseparability parameterMeasured value
    EPR state(1,12,1)(90°, 0°)[Δ(x̂1x̂2)]2+[Δ(p̂1+p̂2)]20.44 ± 0.01
    3-mode GHZ state(1,13,12,1)(90°, 180°, 0°)[Δ(x̂1x̂2)]2+[Δ(p̂1+p̂2+p̂3)]20.65 ± 0.01
    [Δ(x̂2x̂3)]2+[Δ(p̂1+p̂2+p̂3)]20.67 ± 0.01
    [Δ(x̂1x̂3)]2+[Δ(p̂1+p̂2+p̂3)]20.70 ± 0.01
    2-mode cluster state(1,12,1)(90°, 90°)[Δ(p̂1x̂2)]2+[Δ(p̂2x̂1)]20.42 ± 0.01
    3-mode cluster state (graph 1)(1,23,12,1)(90°, 90°, 90°)[Δ(p̂1x̂2)]2+[Δ(p̂2x̂1x̂3)]20.56 ± 0.01
    [Δ(p̂3x̂2)]2+[Δ(p̂2x̂1x̂3)]20.54 ± 0.01
    [Δ(p̂1p̂3)]2+[Δ(p̂2x̂1x̂3)]20.60 ± 0.01
    3-mode cluster state (graph 2)(1,13,12,1)(90°, 180°, 90°)[Δ(p̂1x̂3)]2+[Δ(p̂3x̂1x̂2)]20.69 ± 0.01
    [Δ(p̂2x̂3)]2+[Δ(p̂3x̂1x̂2)]20.65 ± 0.01
    [Δ(p̂1p̂2)]2+[Δ(p̂3x̂1x̂2)]20.63 ± 0.01

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