The uncertainty principle, a jewel at the heart of quantum theory, has been expressed by completely different forms, such as universal uncertainty relations, an uncertainty principle in the presence of quantum memory and a fine-grained uncertainty relation. We unify these uncertainty relations based on a special formalization of probability relations, namely introducing quasi-fine-grained uncertainty relations (QFGURs), which combine different measurements performed on spacelike-separated systems. Our generalized probability relations determine whether a quantum measurement exhibits typical quantum correlations and reveal a fundamental connection between basic elements of quantum theory, specifically, uncertainty measures, combined outcomes for different measurements, quantum memory, entanglement and Einstein-Podolsky-Rosen steering. Furthermore, we derive a universal form for entanglement and steering inequalities explicitly by applying our QFGURs.

中文翻译：

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准细粒度不确定性关系

作为量子理论核心的一颗明珠，测不准原理已经以完全不同的形式表现出来，例如普遍测不准关系、存在量子记忆的测不准原理和细粒度测不准关系。我们基于概率关系的特殊形式化来统一这些不确定性关系，即引入准细粒度不确定性关系 (QFGUR)，它结合了在类空间分离系统上执行的不同测量。我们的广义概率关系决定了量子测量是否表现出典型的量子相关性，并揭示了量子理论基本要素之间的基本联系，特别是不确定性测量、不同测量的组合结果、量子记忆、纠缠和爱因斯坦-波多尔斯基-罗森转向。此外，