Multiparty Quantum Correlations: Classification and Physical Interpretation

该项目将开发一个关于如何量化共享联合量子态的多方之间的相关性的原则性理论。这一理论将被应用于回答有关量子通信网络和量子系统的物理问题，这些问题具有抗噪声特性的新型量子相关性。解决量子网络理论中的问题将导致在具有有限和噪声通信链路的分布式节点网络中传输和存储量子态的更好策略。反过来，这样的网络可以用于经典数据的安全通信、提高精度的分布式传感和改进经典数据的通信速率。新的抗噪声量子相关理论可以为我们指明具有非凡性能的新材料，甚至可能是量子态的自然存储设备。也许最重要的是，这个项目将回答有关多个量子系统之间相关性本质的基本问题。多方关联理论的发展将基于这样一种观点，即无论关联是什么，单个当事方的局部行动不能增加多方系统中的关联量。利用线性规划理论，本项目将基于熵对所有这些相关度量进行分类。这种对基于熵的相关度量的关注使得该理论特别适合于噪声网络通信问题和凝聚态系统中拓扑顺序的分类。需要解决的具体问题包括在两个发送者和一个接收者的量子网络中找到最佳通信速率，量子网络中的分布式数据压缩，以及在大于2的空间维度上量化拓扑顺序。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。

This project will develop a principled theory of how to quantify correlations between multiple parties sharing a joint quantum state. This theory will be applied to answer questions about quantum communication networks and the physics of quantum systems with novel quantum correlations that have noise-resistant properties. Tackling questions in the theory of quantum networks will lead to better strategies for transmitting and storing quantum states in a distributed network of nodes with limited and noisy communication links. Such a network could, in turn, be used for secure communication of classical data, distributed sensing with enhanced precision, and improved communication rates for classical data. The theory of novel noise-resistant quantum correlations could point us toward new materials with remarkable properties, perhaps even natural memory devices for quantum states. Perhaps most importantly, this project will answer fundamental questions about the nature of correlations between multiple quantum systems.The theory of multiparty correlations will be developed based on the idea that, whatever a correlation is, a local action by a single party cannot increase the amount of correlation in a multiparty system. Using the theory of linear programming, this project will classify all such correlation measures based on entropies. This focus on entropy-based correlation measures makes the theory particularly well-suited to problems in noisy network communication and the classification of topological order in condensed matter systems. Specific problems to be tackled include finding the best rates of communication in a quantum network with two senders and one receiver, distributed data compression in a quantum network, and quantifying topological order in spatial dimension greater than two.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.