The Einstein–Podolsky–Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of a local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of “quantum nonlocality,” which manifests itself in three types: quantum entanglement, quantum steering, and Bell’s nonlocality. Although Bell’s nonlocality is more often used to show “quantum nonlocality,” the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality, thus making it amenable to experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is friendlier for experimental implementation, i.e., one may measure the observables only in the $x$, $y$, or $z$ axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.

中文翻译：

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爱因斯坦-波多尔斯基-罗森论证的转向悖论及其扩展的不等式

爱因斯坦-波多尔斯基-罗森 (EPR) 悖论是量子基础的里程碑之一，源于缺乏对量子力学的局部现实描述。EPR悖论激发了“量子非局域性”的重要概念，它表现为三种类型：量子纠缠、量子转向和贝尔非局域性。尽管贝尔非局域性更常用于表示“量子非局域性”，但最初的 EPR 悖论本质上是一个转向悖论。在这项工作中，我们将原始的 EPR 转向悖论表述为一个矛盾等式，从而使其易于实验验证。我们在两个量子比特场景中对转向悖论进行了实验测试。此外，从转向悖论开始，$X$, $是$， 或者 $z$Bloch 球体的轴，而不是其他任意方向。我们还进行了实验来证明这个方案。在实验误差范围内，实验结果与理论预测一致。我们的结果加深​​了对量子基础的理解，并提供了一种检测量子态可控性的有效方法。