Multiparty Quantum Correlations: Classification and Physical Interpretation

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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.