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Scattering as a Quantum Metrology Problem: A Quantum Walk Approach.

Francesco Zatelli1, Claudia Benedetti1, Matteo G A Paris1,2

  • 1Dipartimento di Fisica 'Aldo Pontremoli', Università degli Studi di Milano, I-20133 Milano, Italy.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We explore quantum particle scattering using quantum walks on a lattice. Quantum Fisher information quantifies barrier height estimation accuracy, with a dichotomic measurement offering optimal detection.

Keywords:
optimal measurementquantum Fisher informationquantum metrologyquantum walksscattering

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Quantum information theory

Background:

  • Scattering of quantum particles by potentials is fundamental.
  • Continuous-time quantum walks model quantum transport on lattices.
  • Quantum Fisher information offers a powerful tool for parameter estimation.

Purpose of the Study:

  • To analyze quantum particle scattering by a 1D barrier potential.
  • To quantify the accuracy of barrier height estimation using quantum Fisher information.
  • To investigate the role of initial states and measurement strategies.

Main Methods:

  • Formalized scattering as a continuous-time quantum walk on a lattice with an impurity.
  • Introduced specific initial states for the quantum walker.
  • Derived reflection and transmission probabilities.
  • Utilized quantum Fisher information to assess estimation accuracy.

Main Results:

  • Quantum Fisher information is sensitive to initial wave packet properties (width, momentum).
  • Quantum signal-to-noise ratio exhibits weaker dependency on initial wave packet parameters.
  • A dichotomic position measurement scheme proves nearly optimal for detection.

Conclusions:

  • Continuous-time quantum walks provide a robust framework for scattering problems.
  • Quantum Fisher information effectively quantifies parameter estimation precision.
  • Optimized measurement strategies are crucial for accurate quantum sensing.