Testing the Wineland Criterion with Finite Statistics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909819324071936 |
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| author | Carrera, E. S. Zhang, Y. Bancal, J-D. Sangouard, N. |
| author_facet | Carrera, E. S. Zhang, Y. Bancal, J-D. Sangouard, N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23741 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Testing the Wineland Criterion with Finite Statistics Carrera, E. S. Zhang, Y. Bancal, J-D. Sangouard, N. Quantum Physics 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. |
| title | Testing the Wineland Criterion with Finite Statistics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.23741 |