论文标题
符号二元性，量子斑点和广义高斯人
Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians
论文作者
论文摘要
我们将极性二元性的概念应用于互合形相空间中量子协方差椭圆形的研究。我们特别考虑以前工作中引入的“量子斑点”的情况；量子斑点是与其强的Robertson-schrödinger形式兼容的相空间的最小符号不变区域。我们表明，这些相空间单元的特征是使用极性双重性的简单反射性条件，从而改善了先前的结果。我们将这些几何构造应用于纯高斯状态的表征，从协方差椭圆形的部分信息来看，这使我们能够制定与符号层析成像有关的陈述。
We apply the notion of polar duality from convex geometry to the study of quantum covariance ellipsoids in symplectic phase space. We consider in particular the case of "quantum blobs" introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle in its strong Robertson--Schrödinger form. We show that these phase space units can be characterized by a simple condition of reflexivity using polar duality, thus improving previous results. We apply these geometric constructions to the characterization of pure Gaussian states in terms of partial information on the covariance ellipsoid, which allows us to formulate statements related to symplectic tomography.
