In 1935, in a paper~ entitled ``Can quantum-mechanical description of reality be considered complete?", Einstein, Podolsky, and Rosen (EPR) formulated an apparent paradox of quantum theory. They considered two quantum systems that were initially allowed to interact, and were then later separated. A measurement of a physical observable performed on one system then had to have an immediate effect on the conjugate observable in the other system – even if the systems were causally disconnected! The authors viewed this as a clear indication of the inconsistency of quantum mechanics. In the parton model~ of the nucleon formulated by Bjorken, Feynman, and Gribov, the partons (quarks and gluons) are viewed by an external hard probe as independent. The standard argument is that, inside the nucleon boosted to an infinite-momentum frame, the parton probed by a virtual photon with virtuality $Q$ is causally disconnected from the rest of the nucleon during the hard interaction. Yet, the parton and the rest of the nucleon have to form a colour-singlet state due to colour confinement, and so have to be in strongly correlated quantum states – we thus encounter the EPR paradox at the sub-nucleonic scale. In this paper, we propose a resolution of this paradox based on the quantum entanglement of partons. We devise an experimental test of entanglement, and carry it out using data on proton-proton collisions from the Large Hadron Collider (LHC). Our results provide a strong direct indication of quantum entanglement at sub-nucleonic scales.

中文翻译：

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爱因斯坦-波多尔斯基-罗森悖论和亚核子尺度的量子纠缠

1935年，爱因斯坦，波多尔斯基和罗森（EPR）在题为《对现实的量子力学描述能被认为是完整的吗？》的论文中，提出了一个明显的量子理论悖论，他们认为两个量子系统最初被允许在一个系统上进行的物理可观察测量结果必须立即对另一系统上的共轭可观察结果产生影响，即使这些系统因果断连也是如此！在由Bjorken，Feynman和Gribov提出的核子的parton模型中，一个外部硬探针将parton（夸克和胶子）视为独立的，标准的论点是在核子内部提升到无限动量的框架具有虚拟性的虚拟光子探测的parton$问$在硬相互作用过程中，它与其他核子因果关系断开。但是，由于色域的限制，部分子和其他核子必须形成色单态，因此必须处于强相关的量子态–因此，我们在亚核子级遇到了EPR悖论。在本文中，我们提出了一种基于partons量子纠缠的悖论的解决方案。我们设计了一个纠缠实验，并使用来自大型强子对撞机（LHC）的质子-质子碰撞数据进行了纠缠。我们的结果为亚核子尺度的量子纠缠提供了强有力的直接指示。