Testing the Wineland Criterion with Finite Statistics

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.