International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-309 Gdańsk, Poland.
Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5.
Phys Rev Lett. 2023 Jun 9;130(23):230201. doi: 10.1103/PhysRevLett.130.230201.
The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.
不相容测量的存在通常被认为是量子理论的一个特征，表明其与任何经典世界观不一致。为了证明经典性在科亨-斯佩克尔非定域性意义上的失败，确实需要一组不相容的测量。然而，更广泛适用的经典性概念是存在广义非定域本体论模型。特别是，即使在单个非投影测量中，这个概念也可以对结果的表示施加约束。我们利用这一事实证明，测量不相容性既不是证明广义非定域性失败的必要条件，也不是充分条件。此外，我们表明，在量子准备测量场景中证明广义非定域性失败的每一个证明都可以转换为在没有不相容测量的相应场景中证明广义非定域性失败的证明。
