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Quantum phase estimation using path-symmetric entangled states.

Su-Yong Lee1,2, Chang-Woo Lee1, Jaehak Lee3

  • 1School of Computational Sciences, Korea Institute for Advanced Study, Hoegi-ro 85, Dongdaemun-gu, Seoul 02455, Korea.

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|July 27, 2016
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Summary
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This study explores phase estimation using entangled states, revealing that super-Poissonian states can indefinitely lower the quantum Cramer-Rao bound. Photon-counting measurements achieve this bound, offering robust quantum phase sensing.

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Area of Science:

  • Quantum Information Science
  • Quantum Metrology
  • Quantum Optics

Background:

  • Phase estimation is crucial for quantum sensing.
  • Entangled states offer enhanced measurement precision.
  • Energy constraints limit traditional phase estimation.

Purpose of the Study:

  • Investigate phase estimation sensitivity with path-symmetric entangled states.
  • Identify fundamental limits of phase estimation under energy constraints.
  • Explore the role of photon statistics in achieving the quantum Cramer-Rao bound.

Main Methods:

  • Utilized a generic class of path-symmetric entangled states: |φ〉|0〉 + |0〉|φ〉.
  • Analyzed the quantum Cramer-Rao bound (QCRB) based on component state photon statistics.
  • Proposed and analyzed photon-counting and parity measurements.
  • Introduced a specific component state for optimal QCRB and robustness analysis.

Main Results:

  • The QCRB can be indefinitely lowered by increasing the super-Poissonianity of the component state |φ〉.
  • Full photon-counting measurements achieve the QCRB across all phase shifts [0, 2π].
  • Parity measurements achieve the QCRB within a confined range of phase shifts.
  • A specific component state allows arbitrarily small QCRB with finite energy and offers robustness against photon loss.

Conclusions:

  • Path-symmetric entangled states, particularly those with super-Poissonian characteristics, are powerful resources for high-precision phase estimation.
  • Photon-counting measurements are optimal for achieving the fundamental QCRB with these states.
  • The proposed component state represents an ideal resource for robust and precise quantum phase sensing.