Quantum Gravity and Quantum Information

这个项目位于量子引力和量子信息的接口。这两个子领域的交叉是理论物理学中与引力和量子力学之间的界面有关的许多基础结果的根源。该项目的目标是开发新的量子信息方法，并将其应用于时空量子性质的探索。这项研究的结果预计将对环圈量子引力（LQC）的发展产生直接影响，该理论将引力与自然界所有其他力统一起来，并对理解这些力在早期宇宙中的相互作用产生直接影响。将凝聚态物理学的方法应用于自旋网络状态，以识别支持具有长程关联的量子几何的运动学希尔伯特空间的角。特别是，典型性和本征态热化在一个新的费米表示的自旋1/2截断。在动力学水平上，因果网络的方法被应用到自旋泡沫，以确定具有固定的全局因果结构的配置类别，并确定理论的有效拉格朗日。在微扰水平上，研究了宇宙时空中量子场的纠缠产生，重点研究了前暴胀阶段。其目标是确定量子信息量，如时空区域之间的互信息，描述非微扰量子引力相和微扰有效场论制度之间过渡的普遍特征。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This project lies at the interface of quantum gravity and quantum information. The cross-fertilization of these two sub-fields is at the roots of a number of foundational results in theoretical physics related to the interface between gravity and quantum mechanics. The goal of this project is to develop new quantum-information methods and apply them to the exploration of the quantum nature of spacetime. The results of this research are expected to have a direct impact on the development of loop quantum gravity (LQC), a theory that unifies gravitation with all the other forces of nature, and of the understanding of the interplay between these forces in the very early universe.In the context of loop quantum gravity, methods from condensed-matter physics are applied to spin-network states to identify the corner of the kinematical Hilbert space which supports quantum geometries with long-range correlations. In particular, typicality and eigenstate thermalization in a new fermionic representation of the spin 1/2 truncation is employed. At the dynamical level, methods from causal networks are applied to spin-foams to identify classes of configurations with a fixed global causal structure and determine the effective Lagrangian of the theory. At the perturbative level, the entanglement production by quantum fields in cosmological spacetimes is studied, with a focus on the pre-inflationary phase. The objective is to identify quantum-information quantities, such as the mutual information between regions of spacetime, that describe universal features of the transition between the non-perturbative quantum gravity phase and the perturbative effective-field-theory regime.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.