Catani Lorenzo, Leifer Matthew, Scala Giovanni, Schmid David, Spekkens Robert W
Electrical Engineering and Computer Science Department, Technische Universität Berlin, 10587 Berlin, Germany.
Institute for Quantum Studies and Schmid College of Science and Technology, Chapman University, One University Drive, Orange, California, 92866, USA.
Phys Rev Lett. 2022 Dec 9;129(24):240401. doi: 10.1103/PhysRevLett.129.240401.
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli X and Pauli Z observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that its predictability tradeoff describes a section of a circle is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.
不确定性关系表达了对单个状态上不同测量结果能够联合预测的程度的限制。量子理论中存在非平凡的不确定性关系，通常被认为是它背离经典世界观的一种方式。然而，这一观点受到以下事实的削弱：存在一些操作理论，它们表现出非平凡的不确定性关系，但就其允许广义非语境本体模型而言，它们与经典世界观是一致的。这就引发了一个问题：不确定性关系的哪些方面（如果有的话）不能以这种方式实现，从而构成真正非经典性的证据。我们在此考虑描述一对二元结果测量（例如量子理论中泡利X和泡利Z可观测量的测量）可预测性之间权衡的不确定性关系。我们表明，对于一类满足特定对称性质的理论，这种可预测性权衡的函数形式受非语境性限制在一条线性曲线以下。由于量子比特量子理论具有相关的对称性质，其可预测性权衡描述为一个圆的一部分这一事实违反了这个非语境界限，因此构成了不确定性关系的函数形式如何见证语境性的一个例子。我们还推导了对量子理论的一组选定操作陪衬的影响，并考虑了对三个测量的推广。
