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arXiv · 2504.01910

Joint estimation of position and momentum with arbitrarily high precision using non-Gaussian states

Massimo Frigerio·Matteo G. A. Paris·Carlos Ernesto Lopetegui·Mattia Walschaers
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Abstract

We address the joint estimation of changes in the position and linear momentum of a quantum particle or, equivalently, changes in the complex field of a bosonic mode. Although these changes are generated by non-commuting operators, we show that leveraging non-Gaussianity enables their simultaneous estimation with arbitrarily high precision and arbitrarily low quantum incompatibility. Specifically, we demonstrate that any pure non-Gaussian state provides an advantage over all Gaussian states, whether pure or mixed. Moreover, properly tuned non-Gaussian mixtures of Gaussian states can also serve as a resource.

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Massimo Frigerio, Matteo G. A. Paris, Carlos Ernesto Lopetegui, Mattia Walschaers. 2025-04-04. Joint estimation of position and momentum with arbitrarily high precision using non-Gaussian states. https://arxiv.org/abs/2504.01910

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