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

量子纠缠是量子信息理论的核心概念，也是推动量子技术发展的应用中的关键资源。尽管人们对量子纠缠的理解越来越深入，并且它的许多潜在用途也越来越广泛，但量子纠缠理论仍然是量子科学中一个活跃的、具有挑战性的基础研究领域。非定域博弈提供了一个很有见地的平台，在这个平台上可以量化纠缠作为通信资源，并分析加密协议的安全性。非定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。这些联系与量子密码学中的大量应用一起，激发了当前全球努力发展量子信息科学中非局域博弈的理论和应用。拟议的研究将大大有助于这一努力，（1）建立新的定量工具，从非交换分析来衡量二分纠缠作为一种资源，（2）开发新的方法来提高不可克隆加密协议的安全性分析。卡尔顿大学、特拉华州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和不可克隆加密的算子理论方法方面的领导地位。它还将为量子密码学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.