CAREER: New Frontiers in Quantum Protocols, Operator Algebras, and Property Testing

在过去的十年中，对量子多证明者交互证明（QMIPs）的研究加深了对量子纠缠作为一种信息处理资源的力量的理解。这项研究导致了最近的量子复杂性结果，称为MIP* = RE，它表征了qmip的计算能力。令人惊讶的是，这种表征为数学物理和算子代数中长期存在的问题提供了答案。受此启发，本项目旨在探索复杂性理论、量子信息和纯数学之间的迷人联系。总体主题是研究经典用户如何测试和表征复杂的量子对象，应用范围从密码学到算子代数。这些调查将刺激跨计算机科学、物理和数学的跨学科研究。除了领导研究之外，PI还将向各种各样的社区（包括学术界和工业界）传播这一主题。PI还将参与面对面和在线的推广和教育活动，以促进高中生和本科生对量子信息科学的兴趣。该项目将追求三个主要方向。首先，PI将开发新的协议，允许经典用户验证不可信量子设备中的复杂量子纠缠，应用于纠缠理论和噪声量子计算机的测试。其次，PI将进一步发展MIP* = RE证明中使用的技术，以解决与Tsirelson问题和Connes嵌入问题解决相关的数学未解决问题。第三，PI将启动性质测试的非交换模型的系统研究，该模型将检查局部经典测试如何约束复杂的量子对象。这项研究将建立在PI先前关于测试量子纠缠器件的交互协议的工作之上。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Over the past decade, the study of quantum multiprover interactive proofs (QMIPs) has deepened the understanding of the power of quantum entanglement as an information-processing resource. This research led to a recent quantum complexity result, known as MIP* = RE, which characterizes the computational power of QMIPs. Surprisingly, this characterization yields answers to longstanding problems in mathematical physics and operator algebras. Motivated by this, this project aims to explore the fascinating connections between complexity theory, quantum information, and pure mathematics. The overarching theme is to investigate how classical users can test and characterize complex quantum objects, with applications ranging from cryptography to operator algebras. These investigations will spur interdisciplinary research across computer science, physics, and mathematics. In addition to leading the research, the PI will disseminate this subject matter to a wide variety of communities (both academic and industrial). The PI will also participate in outreach and education activities, both in-person and online, to promote interest in quantum information science in high school and undergraduate students.This project will pursue three main directions. First, the PI will develop novel protocols that allow a classical user to verify complex quantum entanglement in untrusted quantum devices, with applications to entanglement theory and testing of noisy quantum computers. Second, the PI will further develop the techniques used in the proof of MIP* = RE to address unsolved questions in mathematics related to the resolutions of Tsirelson’s problem and Connes’ embedding problem. Third, the PI will initiate the systematic study of a noncommutative model of property testing, which will examine how local classical tests can constrain complex, quantum objects. This research will build upon prior work of the PI on interactive protocols for testing quantum entangled devices.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.