In questioning the completeness of quantum mechanics, Einstein–Podolsky–Rosen (EPR) claimed that from the outcomes of local experiments performed on an entangled system, it was possible to ascribe simultaneous reality to the values of certain incompatible observables. As EPR acknowledged, the inevitable disturbance of quantum measurements prevents the precise verification of these assertions on a single system. However, the EPR elements of reality can still be tested at the ensemble level through weak measurements—which minimally disturb the measured system—by interpreting the EPR assertions as assertions about weak values that follow from the outcomes of projective measurements. Here, we report an implementation of such a test through joint weak measurements followed by post-selection on polarization-entangled photon pairs. Our results show that there is a correspondence between the obtained joint weak values and the inferred elements of reality in the polarization version of the EPR assertions.

在质疑量子力学的完整性时，爱因斯坦-波多尔斯基-罗森（EPR）声称，根据在纠缠系统上进行的局部实验的结果，可以将同时存在的现实归因于某些不兼容的可观测量的值。正如EPR所承认的那样，不可避免的量子测量干扰会阻止在单个系统上对这些断言的精确验证。但是，通过将EPR断言解释为由投影测量结果得出的关于弱值的断言，仍然可以通过弱测量在整体级别上测试现实的EPR元素，从而最小程度地干扰被测系统。在这里，我们报告了通过联合弱测量，然后对偏振纠缠的光子对进行后选择的这种测试的实现。