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

在过去的十年中，量子多验证器交互式证明（QMIP）的研究加深了对量子纠缠作为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，这种特征产生了数学物理和算子代数中长期存在的问题的答案。受此启发，该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。首要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，物理学和数学的跨学科研究。除了领导研究外，PI还将向各种各样的社区（学术和工业）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，以提高高中和本科生对量子信息科学的兴趣。首先，PI将开发新的协议，允许经典用户在不可信的量子设备中验证复杂的量子纠缠，并将其应用于纠缠理论和噪声量子计算机的测试。第二，PI将进一步开发用于证明MIP* = RE的技术，以解决与Tsirelson问题和Connes嵌入问题的解决方案相关的数学中未解决的问题。第三，PI将启动一个非交换性质测试模型的系统研究，这将研究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之前的工作上，用于测试量子纠缠设备的交互协议。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.