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Testing the Wineland Criterion with Finite Statistics.

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This study introduces a hypothesis-testing framework to detect spin-squeezed states using the Wineland parameter. Most experiments could not reject the null hypothesis of non-spin-squeezed states, indicating challenges in confirming spin squeezing with limited data.

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Area of Science:

  • Quantum metrology
  • Atomic physics
  • Statistical analysis

Background:

  • The Wineland parameter is crucial for identifying spin-squeezed states, essential for metrology.
  • Efficient practical estimation strategies and the impact of finite measurements on this parameter are not well-understood.

Purpose of the Study:

  • To formulate spin squeezing detection as a hypothesis-testing problem.
  • To derive bounds on the p-value for quantifying statistical evidence against non-spin-squeezed states.
  • To address the effects of finite statistics in experimental measurements.

Main Methods:

  • Formulating spin squeezing detection as a hypothesis-testing problem.
  • Deriving upper and lower bounds on the p-value.
  • Applying a statistical test to experimental data.

Main Results:

  • In most experimental cases, the hypothesis of non-spin-squeezed states could not be rejected at a 5% significance level.
  • An explicit non-spin-squeezed state was identified that reproduced experimental results with a p-value greater than 5%.
  • The study provides a rigorous method for establishing statistical evidence of spin squeezing.

Conclusions:

  • Current experimental data, under the proposed framework, often fails to provide strong evidence for spin-squeezed states.
  • The developed statistical test offers a robust approach for future experiments to rigorously assess spin squeezing.
  • Finite statistics significantly impact the ability to confirm spin-squeezed states using the Wineland parameter.