论文标题
量子复杂性和全息图
Quantum Complexity and Holography
论文作者
论文摘要
该论文开发了有关所谓的体积复杂性和动作复杂性猜想的最新工作。根据这个建议家族，几何量可以在某些全息引力理论中定义，这些理论可以用双量子力学理论的量子复杂性概念来映射。 在这项工作中，我们回顾了在寻找量子重力理论中使用量子信息理论的原始动机，并主张将全息复杂性作为一种有希望的新工具，可以在阐明黑洞的性质中发挥关键作用。 引入后，我们花了一些时间研究了各种起源的“外来”热力学系统，以期望面对猜想，并寻求全息复杂性的新行为，以帮助我们理解或完善现有的建议。 接下来，我们将注意力转移到对奇异空间的全息复杂性的研究中，定义了对猜想的略微修改版本，这些版本非常适合奇异性，并寻找这些设置中复杂性动态的普遍行为。 最后，我们完成了一些关于全息复杂性与旧表征标准之间有关奇异性的关系的猜测。
This thesis develops recent work on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, geometric quantities can be defined in some holographic gravitational theories that can be mapped with the concept of quantum complexity for states in a dual quantum-mechanical theory. In this work, we review the original motivations for the use of quantum-information theory in the search of a theory of quantum gravity, and argue in favour of holographic complexity as a promising new tool that could play a key role in the elucidation of the properties of black holes. After this introduction, we devote some time to the study of `exotic' thermodynamical systems of diverse origin, confronting the conjectures with expectations and seeking for new behaviours of holographic complexity that could help us understand or refine the existing proposals. Next, we turn our attention to the study of holographic complexity for singular spacetimes, defining slightly modified versions of the conjecture that are well adapted to singularities and searching for universal behaviours of complexity dynamics within these setups. Finally, we finish with some speculations about the relation between holographic complexity and older characterization criteria for singularities in general relativity.
