Non-commutative analysis of non-local games and quantum security

量子纠缠是量子信息理论中的核心概念，也是推动量子技术发展的应用中的关键资源。虽然人们对量子纠缠的概念及其潜在用途的理解越来越深入，但量子纠缠理论仍然是量子科学中一个活跃、具有挑战性和基础性的研究领域。非局域游戏为量化纠缠作为通信资源和分析加密协议的安全性提供了一个有洞察力的平台。非局域博弈理论最近揭示了量子纠缠和非对易分析之间的深刻联系。这些联系，加上量子密码学中的大量应用，推动了当前全球努力发展量子信息科学中非局部博弈的理论和应用。这项研究将通过(1)从非对易分析中建立新的量化工具来测量作为资源的两方纠缠，以及(2)开发新的方法来改进不可克隆加密协议的安全性分析，从而为这一努力做出重要贡献。卡尔顿大学、特拉华大学和查尔默斯理工大学(哥德堡)之间的合作将加强加拿大在非本地游戏以及不可克隆加密的运营商理论方法方面的领先地位。它还将为量子密码学中的后续合作和新应用奠定基础。

Quantum entanglement is a central notion in quantum information theory and a key resource in the applications that are driving efforts to develop quantum technologies. While there is a growing depth of understanding of the concept and its many potential uses, the theory of quantum entanglement remains an active, challenging, and fundamental area of investigation in quantum science.Non-local games provide an insightful platform on which to quantify entanglement as a resource for communication and to analyze the security of encryption protocols. The theory of non-local games recently revealed profound connections between quantum entanglement and non-commutative analysis. These connections together with the plethora of applications in quantum cryptography have motivated a current global effort to develop the theory and applications of non-local games in quantum information science. The proposed research will significantly contribute to this effort by (1) establishing new quantitative tools from non-commutative analysis to measure bipartite entanglement as a resource, and (2) developing novel methods to improve the security analysis of uncloneable encryption protocols. The collaboration between Carleton University, the University of Delaware and Chalmers University of Technology (Gothenburg) will strengthen Canada's leadership in the operator theoretic approach to non-local games as well as uncloneable encryption. It will also set the stage for subsequent collaborations and novel applications in quantum cryptography.