The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.

中文翻译：

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量子上下文和不确定性

测量环境在量子中比在经典物理学中具有更直接的意义，在经典物理学中，对于执行良好的测量，它们可以被忽略。在量子力学中，测量系统的测量设备加环境的配置是其作为量子可观察量的形式化的重要部分。最近，针对清晰的量子可观测值，通过对应于一组清晰的目标可观测值的测量的等价类，对上下文进行了直接的形式化。在这里，我们展示了量子上下文，测量结果对测量量子系统外部环境的依赖性，不仅可以表现为对尖锐可观测值或估值的不同测量的严格排他性，而且可以通过广义量子可观测值的同时测量的性质统计的定量差异来表现出来，通过共存的广义可观测值来形式化量子上下文，而不仅仅是其兼容的尖锐可观测值的子集. 在这里，然后解决了这种量子上下文是否遵循基本量子原理的问题，并且表明不确定性原则对于至少一种形式的非平凡上下文是足够的。因此，情境性被视为量子力学的一个自然特征，而不是仅仅从不可能的测量、抽象哲学问题、隐藏变量理论或其他替代方案的考虑中产生的东西，