Research ArticlePHYSICS

An experimental quantum Bernoulli factory

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Science Advances  25 Jan 2019:
Vol. 5, no. 1, eaau6668
DOI: 10.1126/sciadv.aau6668
  • Fig. 1 The classical Bernoulli factory.

    (A) Concept of sampling task. A sequence of iid coins, with an unknown bias p, are sampled and processed producing a new coin of bias f(p). (B) Doubling function f^(p) = 2p, as per Eq. 1. The dashed blue plot shows the ideal function, which cannot be constructed classically. The workaround is to truncate the function by ε, shown by the solid red line.

  • Fig. 2 Experimental arrangement for the QBF using joint measurements of two p-quoins.

    A pair of H-polarized photons are generated via type I down-conversion in a nonlinear BiBO crystal. They are sent (indicated by red arrows) to a Bell-state analyzer arrangement containing additional MHWP, which set the bias value of each p-quoin, and QWPs, one at OA + 45° and one at OA − 45°, which enables |ψ+〉 and |ϕ〉 to be identified. The photons interfere on a 50:50 NPBS, while the PBS enable H- and V-polarized photons to be separated spatially before being detected using single-photon APDs. Detection events are time-tagged and analyzed using a computer.

  • Fig. 3 Experimental data for the two-qubit QBF.

    The function f^(p) = 2p is constructed using joint measurements of two p-quoins for (A) kmax = 1, (B) kmax = 10, (C) kmax = 100, and (D) kmax = 2000. The dotted blue lines are the ideal theoretical functions, and the red lines represent a model taking experimental imperfections into consideration. Error bars were too small to be included (see Materials and Methods). (E) Mean p-quoin consumption for kmax = 2000.

  • Fig. 4 Construction of f^(p) = 2p using single-qubit measurements of p-quoins.

    (A) The algorithm we use (see the Supplementary Materials). The upper (lower) branch begins with the measurement of the p-quoin in the Z-basis (X-basis). Dashed red (blue) arrows indicate a heads (tails) outcome of the quoin toss. Failure to achieve the appropriate outcome requires the protocol to be repeated until success. (B) Experimental arrangement for the QBF using single-qubit measurements of p-quoins. Red arrows indicate photon inputs from the source (not shown). A single photon encounters a MHWP, which sets p. A HWP set to OA enables Z-basis measurements to be performed for each p. The partner photon, which serves as a herald, is detected directly by an APD. Setting the HWP to OA + 22.5 ° results in an X-basis measurement. Two sets of time-tag data are recorded, allowing p and q-quoins to be sampled.

  • Fig. 5 Experimental data for the single-qubit QBF.

    The function f^(p) = 2p is constructed using single-qubit measurements of p-quoins for (A) kmax = 1, (B) kmax = 10, (C) kmax = 100, and (D) kmax = 2000. The dotted blue lines are the ideal theoretical functions. Error bars were too small to be included (see Materials and Methods). (E) Mean p-quoin consumption for kmax = 82.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Constructing g1(p) in the single-qubit QBF
    • Section S2. Bernstein polynomial fit of the data
    • Fig. S1. Least-squares fit of f^(p) = 2p.

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