Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark.
Phys Rev Lett. 2009 Dec 4;103(23):230402. doi: 10.1103/PhysRevLett.103.230402. Epub 2009 Dec 2.
It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality--independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quantum observables enables the violation of a Bell inequality and therefore must remain incompatible within any other no-signaling theory. While in the case of von Neumann measurements it is sufficient to use the same pair of observables at both sites, general measurements can require different choices. The main result is obtained by showing that for arbitrary dimension the Clauser-Horne-Shimony-Holt inequality provides the Lagrangian dual of the characterization of joint measurability. This leads to a simple criterion for joint measurability beyond the known qubit case.
众所周知，联合可测可观测量不会导致任何贝尔不等式的违背——这与在其他位置选择的状态和测量无关。在这封信中，我们证明了相反的情况：每一对不相容的量子可观测量都能违反贝尔不等式，因此在任何其他无信号理论中都必须保持不相容。虽然在冯·诺依曼测量的情况下，在两个位置使用相同的可观测量就足够了，但一般的测量可能需要不同的选择。主要结果是通过证明对于任意维度，克劳瑟-霍恩-西蒙尼-霍尔特不等式为联合可测性的特征提供了拉格朗日对偶，从而得出了超越已知量子位情况的联合可测性的简单判据。
