Testing the Wineland Criterion with Finite Statistics

• URL: http://arxiv.org/abs/2410.23741v2
• Date: Mon, 05 May 2025 09:39:10 GMT
• Title: Testing the Wineland Criterion with Finite Statistics
• Authors: E. S. Carrera, Y. Zhang, J-D. Bancal, N. Sangouard,
• Abstract summary: Wineland parameter aims at detecting metrologically useful entangled states, called spin-squeezed states, from expectations and variances of total angular momenta.<n>We formulate the detection of spin squeezing as a hypothesis-testing problem, where the null hypothesis assumes that the experimental data can be explained by non-spin-squeezed states.<n>By applying our statistical test to data obtained in multiple experiments, we are unable to reject the hypothesis that non-spin squeezed states were measured with a p-value of 5% or less in most cases.
• Score: 0.22499166814992436
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Wineland parameter aims at detecting metrologically useful entangled states, called spin-squeezed states, from expectations and variances of total angular momenta. {However, efficient strategies for estimating this parameter in practice have yet to be determined and in particular, the effects of a finite number of measurements remain insufficiently addressed. We formulate the detection of spin squeezing as a hypothesis-testing problem, where the null hypothesis assumes that the experimental data can be explained by non-spin-squeezed states. Within this framework, we derive upper and lower bounds on the p-value to quantify the statistical evidence against the null hypothesis.} By applying our statistical test to data obtained in multiple experiments, we are unable to reject the hypothesis that non-spin squeezed states were measured with a p-value of 5\% or less in most cases. We also find an explicit non-spin squeezed state according to the Wineland parameter reproducing most of the observed results with a p-value exceeding 5\%. More generally, our results provide a rigorous method to establish robust statistical evidence of spin squeezing from the Wineland parameter in future experiments,accounting for finite statistics.

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