Fisher information from quantum many-particle arrival time measurements

• URL: http://arxiv.org/abs/2505.21214v1
• Date: Tue, 27 May 2025 14:03:42 GMT
• Title: Fisher information from quantum many-particle arrival time measurements
• Authors: Jukka Kiukas, Andreas Ruschhaupt,
• Abstract summary: We formulate a quantum arrival time measurement process for a Bosonic many-particle system, with the aim of extracting statistical information on single-particle properties.<n>We find the resulting probability distributions for arrival time sequences, which we consider as parametric models for the statistical inference of single-particle parameters.<n>We observe that even though no information remains in the spatial distribution, the single-particle momentum is indeed identifiable from the arrival time data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We formulate a quantum arrival time measurement process for a Bosonic many-particle system, with the aim of extracting statistical information on single-particle properties. The arrival time is based on a dynamical multi-particle absorption model in the Fock space, and we consider systems in coherent and incoherent mixtures of $N$-particle states. We find the resulting probability distributions for arrival time sequences, which we consider as parametric models for the statistical inference of single-particle parameters, and derive a tractable expression for the associated (classical) Fisher information. Subsequently focusing on the concrete case of the momentum parameter of a 1D particle, we consider the idealized limits of a point (Dirac delta) detector and an infinite particle system forming a spatially uniform ``beam''. We observe that even though no information remains in the spatial distribution, the single-particle momentum is indeed identifiable from the arrival time data, even in the limit of ``sparse beams'' of vanishing particle density, where we obtain simple analytical form for the Fisher information, which, interestingly, coincides with the one obtained from a hypothetical time-stationary detection model. Our results contribute to the fundamental understanding of temporal measurement data arising from quantum systems consisting of freely evolving particles.

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