Quantum Gravity and Entanglement

纠缠是量子力学的独特性质，它阻止了仅仅通过查看系统单个组件的属性来描述系统，它是当前从量子信息科学到凝聚态物理再到量子场论等不同物理领域研究的核心内容。这项研究的主要目的是了解纠缠在描述时空量子性质中的作用。这项工作研究了理论物理中的基本难题，如宇宙原始状态的描述和黑洞蒸发中信息的命运。重点是时空纠缠的普遍方面，这可以为任何量子引力理论提供有价值的见解。在普朗克尺度上，超越爱因斯坦广义相对论的新量子效应有望占据主导地位。圈量子引力是描述这些区域的物理的主要候选理论之一。在这个理论中，时空具有一种颗粒结构，它作为拓扑不变真空的泡沫状激发而产生。从这个角度来看，时空是由“基本成分”组成的，就像在凝聚态物理中一样，它可以有不同的量子相。主要的开放问题是确定描述我们平滑扩展的时空的量子相。最近在凝聚态物理中开发的一套技术将被用来研究量子几何自由度之间的纠缠量。这项研究将直接解决时空的量子性质问题。对纠缠网络态的研究结果将为量子引力中空时态的物理性质提取提供基础。将调查三个方向。第一种是关于Minkowski时空态，其中纠缠网络态是通过变分变换来最小化ADM能量而得到的。第二个方向涉及纠缠网络态在量子宇宙学中的应用，经典奇点附近的纠缠研究，以及De Sitter展开阶段子系统的热化时间。第三个方向是关于黑洞的时空，纠缠熵和黑洞熵之间的关系，以及在蒸发过程中纠缠熵的动力学。

Entanglement, the unique property of quantum mechanics that prevents the description of a system by just looking at the properties of its individual components, is a centerpiece in current research in diverse areas of physics spanning from quantum information science to condensed matter physics to quantum field theory. The main objective of this research is to understand the role of entanglement in the description of the quantum nature of space-time. This works investigates fundamental puzzles in theoretical physics such as the description of the primordial state of the universe and the fate of information in black hole evaporation. The focus is on universal aspects of space-time entanglement that can provide valuable insights for any theory of quantum gravity. At the Planck scale new quantum effects that go beyond Einstein's general relativity are expected to dominate. Loop quantum gravity is one of the leading candidate theories for describing the physics in these regimes. In this theory, space-time has a granular structure that arises as a foam-like excitation of a topologically invariant vacuum. From this perspective, space-time is made of 'elementary constituents' and, as in condensed matter physics, it can have different quantum phases. The main open problem is to identify the quantum phase that describes our smooth extended space-time. A set of techniques that were recently developed in condensed matter physics will be used to study the amount of entanglement between quantum geometry degrees of freedom. This research will directly address the question of the quantum nature of space-time. The results of this research on entangled-network states will provide the basis for extracting physical properties of space-time states in quantum gravity. Three directions will be investigated. The first regards the Minkowski space-time state where the entangled-network state is obtained via a variational ansatz for the minimization of the ADM energy. The second direction regards the use of entangled-network states in quantum cosmology, the study of entanglement near classical singularities, and the thermalization time of subsystems in the de Sitter expansion phase. The third direction regards black hole space-times, the relation between entanglement entropy and black hole entropy, and the dynamics of entanglement entropy in the evaporation process.