标题： 量词和非经典性测量与状态的证据 显示英文标题

标题： Quantifiers and witnesses for the nonclassicality of measurements and of states

摘要： 在最近的工作中，arXiv:2503.05884，我们提出了一种统一的非经典性概念，适用于量子理论中的任意过程，包括单个量子态、测量、通道、这些的集合等。 该概念来源于广义非背景性的原理，但以一种新颖的方式，适用于单个过程而非完整的实验或理论。 在这里，我们提供了新的证书和度量方法，用于表征和量化存在于态、测量及其集合中的非经典性，使用半定规划技术。 这些方法依赖于理论，补充了基于非背景性不等式的理论独立方法。 我们提供了这些思想在许多示例中的具体应用。 显示英文摘要

摘要： In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is derived from the principle of generalized noncontextuality, but in a novel manner that applies to individual processes rather than full experiments or theories. Here, we provide novel certificates and measures for characterizing and quantifying the nonclassicality inherent in states, measurements, and sets thereof, using semidefinite programming techniques. These are theory-dependent, complementing theory-independent methods based on noncontextuality inequalities. We provide explicit applications of these ideas to many illustrative examples.