Markovich Liubov A, Urbanetz Justus, Man'ko Vladimir I
Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
Institute for Information Transmission Problems, Bol. Karetny per. 19, Moscow 127051, Russia.
Entropy (Basel). 2024 Feb 20;26(3):176. doi: 10.3390/e26030176.
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be "quantum".
本文深入探讨了量子态的断层概率密度函数（pdf）表示的重要性，揭示了可作为断层图的特殊pdf类别。与在希尔伯特空间上使用波函数或密度算子不同，作为真正pdf的断层图用于完整描述量子系统的状态。与准pdf（如维格纳函数）不同，断层图可使用经典概率论中所有用于pdf估计的工具进行分析，这有助于实现更高质量的状态重构。在处理pdf为多模的非高斯态时，这一点尤为有用。分布族的知识在参数和非参数密度估计方法的应用中起着重要作用。我们表明，并非所有pdf都能充当量子态的断层图，并介绍了pdf要成为“量子”的必须满足的条件。
