Relativistic Quantum Information: Applications and foundations in Quantum Information, Relativity and Machine Learning

在过去的十年里，出现了一个高研究强度的新领域：相对论量子信息(RQI)。RQI将现代物理学的两大支柱--广义相对论和量子理论与信息论结合在一起。RQI领域的成果从对自然规律的新见解(例如黑洞物理和宇宙学)一直到量子计算和量子安全通信的具体应用。特别是，由于理论和技术上的进步，量子信息处理中的相对论效应的研究最近变得更加重要。量子光学、超导电路和玻色-爱因斯坦凝聚体的实验现在可以探测相对论对量子信息的影响。将纠缠分布在数百公里范围内的协议现在正在达到相对论效应变得重要的状态，卫星实验正在开发中，这些实验将测量引力对量子纠缠的影响。 这一提议旨在研究RQI领域的一些关键理论和应用问题：在量子密码学或量子计算等量子信息技术中，哪些相对论设置比非相对论设置更具优势？量子场的涨落能为量子纠缠提供一个实用的、可再生的来源吗？具体地说，这项拟议的研究调查了在量子场论、超快量子光学和超导电路中仍未探索的区域中的量子信息处理，在这些领域中，爱因斯坦的相对论和量子理论都是理解信息处理和流动的必要条件。 此外，这项拟议的研究还探索了使用深度学习和其他机器学习技术来研究量子场论中的测量和关联。特别是，该提案将研究如何将神经网络应用于使用从粒子探测器与场的局部(在空间和时间上)耦合获得的测量获得的探测数据来对QFT的非局部特征进行分类的问题。其长期目标是开发一种探索相对论量子力学和场论中测量理论的新方法，将理论物理中的深层概念，如量子引力中的全息术和量子场论中的纠缠与最新的数据处理技术相结合。 这些研究将增进我们对量子理论和相对论的基础知识。与此同时，这可能会对加拿大的经济和行业产生重大的长期影响，因为加拿大在机器学习和量子技术方面的专业知识正在发展中。具体地说，将通过理论研究获得的知识应用于量子计算、量子保密通信和开发灵敏度远远超出当前技术限制的测量设备。

Over the past decade, a new field of high research intensity has emerged: Relativistic Quantum Information (RQI). RQI brings together the two pillars of modern physics, general relativity and quantum theory, with information theory. The results in the field of RQI range from new insights into the laws of Nature (e.g. black hole physics and cosmology) all the way to concrete applications in quantum computing and quantum-secured communication. In particular, the study of relativistic effects in quantum information processing has recently become more important due to improvements both in theory and in technology. Experiments in quantum optics, superconducting circuits and Bose-Einstein condensates can now probe relativistic influences on quantum information. Protocols that distribute entanglement over hundreds of kilometers are now reaching regimes where relativistic effects are becoming important, and satellite experiments are being developed that will measure gravitational effects on quantum entanglement. This proposal seeks to investigate some of the key theoretical and applied questions in the field of RQI: Which relativistic settings have an advantage over non-relativistic ones in quantum information technologies such as quantum cryptography or quantum computing? Can the fluctuations of a quantum field provide a practical and renewable source of quantum entanglement? Concretely, the proposed research investigates the processing of quantum information in still unexplored regimes in quantum field theory, ultra-fast quantum optics and superconducting circuits where both Einstein's relativity and quantum theory are necessary to understand the processing and flow of information. Furthermore, the proposed research explores the use of deep learning and other machine learning techniques to study measurements and correlations in quantum field theory. In particular this proposal will investigate how neural networks can be applied to the problem of classifying non-local features of QFTs using probe data from measurements obtained coupling particle detectors locally (in space and time) to the field. The long term objective is to develop a new way of exploring measurement theory in relativistic quantum mechanics and field theory connecting deep notions in theoretical physic such as holography in quantum gravity and the entanglement in quantum field theories with the latest techniques in data processing. These studies will advance our fundamental knowledge of quantum theory and relativity. At the same time, will potentially have a significant long-term impact on Canada's economy and industry developing the Canadian expertise in machine learning and in quantum technologies. Concretely, applying knowledge acquired through the theoretical studies to the development of applications in quantum computing, quantum-secured communication and the development of measurement devices with sensitivities much beyond the limits of current technologies.