量子信息测度及其在量子场论中的应用
Quantum information measures and their applications in quantum field theory
摘要：
在过去的几十年中，人们已经认识到，量子场论（QFT）中的各种各样的现象可以使用量子信息度量来表征，例如状态的纠缠熵和同一希尔伯特空间中的量子态之间的相对熵。在这篇论文中，我们使用这些和其他来自量子信息理论的工具来研究量子场论中的几个有趣的问题。分析的主题范围从使用纠缠熵研究QFT中的Aharonov-Bohm效应，到使用相对熵性质的Ryu-Takayanagi公式（在AdS/CFT对偶的背景下提出）的一致性。我们表明，相对熵也可以用来获得新的有趣的量子能量不等式，限制负能量密度的空间分布。
英文摘要：
In the last decades, it has been understood that a wide variety of phenomena in quantum field theory (QFT) can be characterised using quantum information measures, such as the entanglement entropy of a state and the relative entropy between quantum states in the same Hilbert space. In this thesis, we use these and other tools from quantum information theory to study several interesting problems in quantum field theory. The topics analysed range from the study of the Aharonov-Bohm effect in QFT using entanglement entropy, to the consistence of the Ryu-Takayanagi formula (proposed in the context of the AdS/CFT duality) using properties of relative entropy. We show that relative entropy can also be used to obtain new interesting quantum energy inequalities, that constrain the spatial distribution of negative energy density.
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