Research ArticlePHYSICS

Probing measurement-induced effects in quantum walks via recurrence

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Science Advances  29 Jun 2018:
Vol. 4, no. 6, eaar6444
DOI: 10.1126/sciadv.aar6444
  • Fig. 1 Illustration of the reset and the continual scheme.

    Schemes illustrating the quantum walk implementation of the reset scheme (A) and the continual scheme with the sinks at x = 0, denoted by black holes (B), both exemplary for a measurement in step 6. Each gray diamond corresponds to the application of the Hadamard coin, followed by the spatial shift.

  • Fig. 2 Schematic of the experimental setup.

    Schematic of the experimental setup of the time-multiplexed quantum walk with active in- and outcoupling realized by two EOMs (see Materials and Methods for details). The active control of the switches allow us to implement in the time domain both the continual and reset schemes, physically equivalent to the spatial representations in Fig. 1 in one setup. HWP, half-wave plate; PBS, polarizing beam splitter; SMF, single-mode fiber; SNSPDs, superconducting nanowire single-photon detectors.

  • Fig. 3 Intensity distributions within step 30 and the evolution over 36 steps for both regimes.

    Top: Intensity distribution in step 30 for the reset scheme (A) and the continual scheme (B). The orange (experimental data) and the red (numerical data) bar charts represent horizontally polarized light, while the light blue (experimental data) and the dark blue (numerical data) bar charts depict vertically polarized light. The errors bars are omitted for clarity (for error analysis, see Materials and Methods). Bottom: Evolution of the experimentally observed intensity distribution over the positions as the walk evolves from step 0 to 36 in a chessboard diagram with a logarithmic color scale. (C) Unitary evolution free of measurements for the reset scheme and (D) conditional evolution with the sinks for the continual scheme. Note that in this last case, we expect a symmetric distribution with respect to the origin, and the remaining asymmetry is due to experimental imperfections in the coin realization and coupling efficiencies for the two polarizations (for a detailed analysis of the experimental inaccuracies, see Materials and Methods).

  • Fig. 4 The experimental results for the recurrence probability in both regimes.

    The experimental results for recurrence probabilities in the reset scheme Embedded Image (red symbols) and the continual scheme Embedded Image (blue symbols). The dashed lines give the numerical values that are to be expected from a numerical simulation of the experiment. The overall deviation between experimental and numerical values in the continual scheme is mainly defined by the deviation in step 4, as the contributions of later steps to the sum are small in comparison to the first four steps. For the error analysis, please refer to Materials and Methods.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Recurrence in classical random walks
    • Signal-to-noise ratio
    • fig. S1. Signal-to-noise ratio of the experimental data.
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