标题： 二维系统的模值的完全表征 显示英文标题

标题： Full characterization of modular values for two-dimensional systems

摘要： Vaidman指出了模值的重要性，并将泡利自旋算符的模值与其在特定耦合强度下的弱值相关联[Phys. Rev. Lett. 105, 230401 (2010)]。如果能将这种关系推广将会很有用，因为模值假设了有限的测量相互作用强度，有时比假设无限小相互作用的弱值更实用。在本文中，我们给出了一个通用表达式，该表达式将二维希尔伯特空间中任意可观测量的弱值和模值在任意耦合强度下的关系进行了关联。利用这个表达式，我们展示了模值的“求和规则失效”，这与弱值的“乘积规则失效”有相似之处。我们给出了一些有趣情况下的“求和规则失效”的例子，即基于非局域性的悖论，包括EPR悖论、Hardy悖论和柴郡猫实验。 显示英文摘要

摘要： Vaidman pointed out the importance of modular values, and related the modular value of a Pauli spin operator to its weak value for specific coupling strengths [Phys. Rev. Lett. 105, 230401 (2010)]. It would be useful if this relationship is generalized since a modular value, which assumes a finite strength of the measurement interaction, is sometimes more practical than a weak value, which assumes an infinitesimally small interaction. In this paper, we give a general expression that relates the weak value and the modular value of an arbitrary observable in the 2-dimensional Hilbert space for an arbitrary coupling strength. Using this expression, we show the "failure of sum rule" for modular values, which has a resemblance to the "failure of product rule" for weak values. We give examples of "failure of sum rule" for some interesting cases, i.e., paradoxes based on nonlocality, which include EPR paradox, Hardy's paradox, and Cheshire cat experiment.