标题： 使用非高斯态对位置和动量进行任意高精度联合估计 显示英文标题

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

摘要： 我们研究了量子粒子位置和线性动量变化的联合估计问题，或者等效地，玻色模复场变化的联合估计问题。尽管这些变化由非交换算符生成，但我们证明，利用非高斯特性能够以任意高的精度和任意低的量子不兼容性同时进行估计。具体而言，我们证明了任何纯非高斯态相对于所有高斯态（无论是纯态还是混合态）都具有优势。此外，适当调谐的高斯态的非高斯混合态也可以作为资源使用。 显示英文摘要

摘要： 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.