论文标题
使用配置空间上的合奏对具有经典设备的量子系统的测量
Measurement of a quantum system with a classical apparatus using ensembles on configuration space
论文作者
论文摘要
找到一种在物理上一致的方法来建模经典和量子系统之间的相互作用是一项高度不平凡的任务。尽管已经提出了许多基于各种数学形式主义的建议，但大多数这些努力都遇到了一种或另一种的困难。 Sudarshan及其合作者给出了第一个详细描述之一，他们在量子力学中的测量问题的激励中提出了希尔伯特 - 量词相互作用的希尔伯特空间表述，这些互动利用了Koopman-Von Neumann对经典系统的描述。在这里，我们使用合奏在配置空间上的方法来详细说明经典设备，以测量以两个局部状态叠加制备的量子粒子的位置。我们表明，经典设备指针的概率留在与量子粒子概率相对应的状态。随后对指针的观察会导致其概率密度的更新。从中，我们可以获取有关量子粒子位置的信息，从而导致其波函数的更新。由于这种形式主义包含不确定性和有限的测量精度，因此非常适合计量应用。此外，它解决了在对设备的量子描述中出现的基本问题。
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus.
