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Gaussian phase sensitivity of boson-sampling-inspired strategies

Antonio A. Valido and Juan José García-Ripoll
Phys. Rev. A 103, 032613 – Published 24 March 2021
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  • INTRODUCTION
  • GAUSSIAN PHASE SENSITIVITY
  • APPLICATION: N-MODE HOMODYNE DETECTION…
  • OUTLOOK AND CONCLUDING REMARKS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    In this paper we study the phase sensitivity of generic linear interferometric schemes using Gaussian resources and measurements. Our formalism is based on the Fisher information. This allows us to separate the contributions of the measurement scheme, the experimental imperfections, and auxiliary systems. We demonstrate the strength of this formalism using a broad class of multimode Gaussian states that includes well-known results from single- and two-mode metrology scenarios. Using this, we prove that input coherent states or squeezing improve upon the nonclassical states proposed in preceding boson-sampling-inspired phase-estimation schemes. We also develop a polychromatic interferometric protocol, demonstrating an enhanced sensitivity with respect to two-mode squeezed-vacuum states, for which the ideal homodyne detection is formally shown to be optimal.

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    • Received 14 September 2020
    • Accepted 8 March 2021

    DOI:https://doi.org/10.1103/PhysRevA.103.032613

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Boson samplingMetrologyQuantum information processing with continuous variablesQuantum metrologyQuantum parameter estimation
    Quantum Information, Science & Technology

    Authors & Affiliations

    Antonio A. Valido* and Juan José García-Ripoll

    • Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain

    • *a.valido@iff.csic.es

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    Vol. 103, Iss. 3 — March 2021

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    Images

    • Figure 1
      Figure 1

      Sketch of a generic N-mode Gaussian phase-estimation strategy consisting of a probe m-mode state, characterized by RS and VS (orange), and an ancilla (N−m)-mode state, characterized by RA and VA (green). Both probe and ancillary systems interact via the interferometer modeled by L, whereafter the first probe mode undergoes the (single) phase rotation φ, such that the whole propagation is described by S(φ). The output modes of the probe system are finally assessed by a generic quadrature measurement determined by ΣS.

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    • Figure 2
      Figure 2

      Left: The roots of the polynomial (38) as functions of the interferometer size N, where the horizontal black line represents the unit value sin2φ0(x)=1. Notice that the solid blue and dashed orange lines do not regard injective functions because the polynomial has two distinct real roots. Central: The FI associated to the position quadrature measurement as a function of the interferometer size and for distinct input probe states: the black-solid, blue-dashed, and orange-dot-dashed lines correspond to the tensor product of coherent (i.e., s1=s2=1), one-mode squeezed⊗coherent (i.e., s1=e2s′ and s2=1), and single-mode squeezed (i.e., s1=s2=e2s′) states, respectively. For a fair comparison, we have fixed the input mean photon number per mode to an identical value for all input states, i.e., n¯≈1.38, and we have chosen the unknown phase shift φ=π/3 and the squeezing parameter s′=1/2. Right: Similarly, the FI as a function of the mean photon number per mode for a fixed squeezing parameter. We have taken the same values for the rest of the parameters.

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    • Figure 3
      Figure 3

      Left: Log plot of the polychromatic QFI as a function of s′ and for distinct values of the modulation parameter ε, shown in the large squeezing regime. We have fixed the transmissivity τ=0. Central: Three-dimensional plot of the deviation associated to the position quadrature measurement for input two-mode squeezed-vacuum states and fixed value of the phase shift φ=π/4. Right: Similarly, the deviation of the FI as a function of φ for a fixed modulation frequency ε=1/2 and two given values of the squeezing parameter: the blue and dashed orange lines correspond to s=0.1 and 0.15, respectively. In the central and left panels, the transmissivity was chosen τ=1/2. Log denotes the natural logarithm.

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