随机系数纯态、密度算符形式体系与策赫问题
Random-coefficient pure states, the density operator formalism and the Zeh problem
AI总结：
本文提出随机系数纯态（RCPS）概念，将其与密度算符形式体系建立联系，并利用随机变量高阶矩解决策赫1970年提出的问题。
摘要：
量子电子学在量子信息处理领域的发展中发挥着重要作用。在该领域中，盲量子源分离和盲量子过程层析成像的发展，已在希尔伯特空间形式体系内引出了随机系数纯态（Random-Coefficient Pure State，RCPS）这一概念：其在选定基底下展开的系数是随机变量。本文首先描述了一个需要引入该概念的实验情形。冯·诺依曼处理统计混合的方法考虑的是可观测量的统计性质，而在存在RCPS的情况下，人们必须处理测量结果概率的统计性质，这些概率本身成为随机变量。本文回顾指出，在存在冯·诺依曼统计混合时，密度算符ρ形式体系的一致性基于一个公设。RCPS概念的意义通过自旋1/2的简单情形下的两个实例加以呈现。量子力学使用者对ρ形式体系的最频繁使用，是建立给定RCPS与密度算符形式体系语言之间某些联系的一个动机，同时须牢记RCPS所描述的情形不同于导致引入ρ的情形。本文确立，朗道—费曼对ρ的使用是在一种既不同于冯·诺依曼统计混合、也不同于RCPS的情形中被调用的。本文表明，利用一个恰当选取的随机变量的高阶矩有助于解决策赫（Zeh）于1970年已经指出的一个问题。
英文摘要：
Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the formalism of the Hilbert space, to the introduction of the concept of a Random-Coefficient Pure State, or RCPS: the coefficients of its development in the chosen basis are random variables. This paper first describes an experimental situation necessitating its introduction. While the von Neumann approach to a statistical mixture considers statistical properties of an observable, in the presence of an RCPS one has to manipulate statistical properties of probabilities of measurement outcomes, these probabilities then being themselves random variables. It is recalled that, in the presence of a von Neumann statistical mixture, the consistency of the density operator \r{ho} formalism is based on a postulate. The interest of the RCPS concept is presented in the simple case of a spin 1/2, through two instances. The most frequent use of the \r{ho} formalism by users of quantum mechanics is a motivation for establishing some links between a given RCPS and the language of the density operator formalism, while keeping in mind that the situation described by an RCPS is different from the one which has led to the introduction of \r{ho}. It is established that the Landau - Feynman use of \r{ho} is mobilized in a situation differing from both the von Neumann statistical mixture and the RCPS. It is shown that the use of the higher-order moments of a well-chosen random variable helps solving a problem already identified by Zeh in 1970.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
