CQIS: Quantum Chaos and Quantum Gravity from Entanglement

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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.