A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2π. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phase observable having several undesirable features, including (i) having a trivially uniform probability density for any state of the system, (ii) not reducing to the periodic case in an appropriate limit, and (iii) not having any clear generalisation to an infinite energy spectrum. In contrast, we note that a covariant time observable has been previously defined for such Hamiltonians, which avoids these features. We also show how this 'quasiperiodic' time observable can be represented as the well-defined limit of a sequence of periodic time observables.
Reply to "Comment on 'Nonlocality claims are inconsistent with Hilbert-space quantum mechanics' '"
在Phys. Rev. A 101，022117（2020）中，有人认为贝尔不等式是基于经典物理学，而不是量子物理学，因此它们在实验中的违反并没有为真实（量子）世界中存在特殊的非局域和超光速影响提供支持。对Lambare的评论的回复，Phys. Rev. A 104，066201（2021），试图澄清与正确使用希尔伯特空间量子力学来识别后来宏观测量结果的微观原因有关的一些问题，贝尔没有正确解决这个问题，他使用经典隐变量代替希尔伯特子空间（相当于，他们的投影仪）采用冯诺依曼在他的\it{Mathematical Foundations of Quantum Mechanics}。
Comment on `Decomposition of pure states of a quantum register'
I. Raptis和R. quant-ph/0010104中的Zapatrin显示了将$l$ -量子位量子寄存器的一般状态表示为至多$2^l-l$产物状态的总和的可能性。本文对任意维数$n$的Hilbert空间的张量积分解提出了一种更简单的构造方法，并有推广的可能性（文中所用的单纯复形不直接应用）。在这种情况下，它是具有$n^l-(n^2-n)l/2$产物状态的分解。
Comment on "Relativistic quantum oscillator model under the effects of the violation of Lorentz symmetry by an arbitrary fixed vector field'' by Faizuddin Ahmed
Facultad de Ciencias Naturales y Matemáticas, Universidad Nacional del Callao（卡亚俄国立大学自然科学与数学学院）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；Universidad Tecnológica del Perú (UTP)（秘鲁理工大学）；Departamento de Ciencias, Universidad Privada del Norte (UPN)（北方私立大学科学系）
Comment on 'Revisiting the phase transitions of the Dicke model'
在Das和Sharma的工作[Phys. Rev. A 105，033716（2022）]中，研究了Dicke模型的相变。其主要结果是，该模型除了表现出已知的量子相变、激发态量子相变和热相变外，还存在一个上界能$E_{*}$，超过这个上界能，该模型不再表现出量子混沌行为，本征函数的结构发生变化.基于这一发现，许多关于Dicke模型的成熟结果受到质疑。我们认为，这一结果及其所有后果是虚假的数值效果，从一个不适当的截断数值对角化所需的无限维希尔伯特空间。
