CQIS: Quantum Chaos and Quantum Gravity from Entanglement

量子力学的一个与直觉相反的特征是，相距遥远的两个粒子可能存在量子纠缠，这是一种非局域关联，比经典力学可能允许的任何东西都要强。爱因斯坦曾将量子纠缠描述为“远距离的诡异行为”。物理学中的另一个基本问题是引力的起源。根据爱因斯坦的广义相对论，物质和能量扭曲时空的方式类似于手指推动气球变形的方式。尽管爱因斯坦理论取得了显著的成功，但它并没有告诉我们为什么我们的时空“气球”会有这样的行为，以及如何用量子力学来描述它。令人惊讶的是，这两个基本的开放问题-量子纠缠和量子引力--可能是一枚硬币的两面。粗略地说，这个想法是量子纠缠是形成时空几何的纤维。两个区域之间有更多的量子纠缠将使它们在空间上更接近彼此。从这个角度来看，物质影响几何是很自然的，因为物质的动力学导致了量子纠缠的演化。已经发现了许多证据支持这一观点，但纠缠和引力之间的二元性背后的一般理论还没有发展出来。这个项目的目标是促进对量子纠缠和量子引力之间联系的理解。更具体地说，PI计划从两个方向研究纠缠-引力对应。第一个方向是应用量子信息论对量子引力有新的理解。虽然目前还不知道如何建立一个完整的量子引力理论，但已经有一些玩具模型展示了这种对应关系的一些特征，同时仍然足够简单，可以进行具体计算。PI计划使用这样的玩具模型，包括Sachdev-Ye-Kitaev模型和随机张量网络模型来研究黑洞内部物理。黑洞是具有强烈引力效应的时空几何的简单例子。信息落入黑洞的命运是一个超越广义相对论的具体问题。这个项目的目标是对如何描述黑洞内部的时空几何以及如何从外部检索内部信息有更微观的理解。这个项目的第二个方向是利用纠缠-引力对应来研究量子信息理论中的新问题。例如，如何定义和探索一般量子多体系统中的因果结构？如何衡量量子动力学的复杂性？量子计算机如何帮助学习量子系统的物理性质？量子信息理论工具和引力理论的见解相结合，带来了解决这些基本问题的新方法，这些问题将在本项目中研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

A counter-intuitive feature of quantum mechanics is that two particles far away can have quantum entanglement, which is a kind of nonlocal correlation that is stronger than anything possibly allowed by classical mechanics. Einstein famously described quantum entanglement as “spooky action at a distance”. Another fundamental question in physics is the origin of gravity. According to Einstein’s general relativity, matter and energy distort the spacetime in a similar way as how pushing with a finger deforms a balloon. Despite the remarkable success of the Einstein theory, it does not tell us why our spacetime “balloon” behaves this way, and how to describe it using quantum mechanics. Surprisingly, these two fundamental open questions---quantum entanglement and quantum gravity---could be two sides of one coin. Roughly speaking, the idea is that quantum entanglement is the fiber that forms the spacetime geometry. Having more quantum entanglement between two regions will make them closer to each other in space. From this point of view, it is natural that matter affects geometry, since the dynamics of matter leads to evolution of quantum entanglement. A lot of evidence has been found to support this idea, but the general theory behind this duality between entanglement and gravity has not been developed. The goal of this project is to advance the understanding to the connection between quantum entanglement and quantum gravity. More specifically, the PI plans to study the entanglement-gravity correspondence in two directions. The first direction is to apply quantum information theory to gain new understanding to quantum gravity. While it remains unknown how to build a complete theory of quantum gravity, there are toy models which demonstrate some feature of this correspondence while still being simple enough for concrete calculations. The PI plans to use such toy models including the Sachdev-Ye-Kitaev model and random tensor network models to study black hole interior physics. Black holes are simple examples of spacetime geometry with a strong gravity effect. The fate of information falling into a black hole is a concrete problem that is beyond general relativity. The goal of this project is to have a more microscopic understanding of how to describe the spacetime geometry in the interior of the black hole, and how to retrieve information in the interior from outside. The second direction of this project is to use the entanglement-gravity correspondence to study new questions in quantum information theory. For example, how to define and probe the causal structure in a general quantum many-body system? How to measure the complexity of quantum dynamics? How can quantum computers help in learning physical properties of a quantum system? A combination of quantum information theory tools and insights from gravity theory brings new ways to address such fundamental questions, which will be studied in this project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.