Quantum information spreading and scrambling in a distributed quantum network: A Hasse/Lamport diagrammatic approach

Large-scale quantum networks, known as quantum internet, hold great promises for advanced distributed quantum computing and long-distance quantum communication. It is essential to have a proper theoretical analysis of the quantum network and explore new applications and protocols that justify building such an extensive network. We propose a novel diagrammatic way of visualizing information flow dynamics within the quantum network, which preserves the causal relationship between different events at different nodes. This facilitates synchronization among network nodes, studies the error propagation, and allows for tracking valuable quantum resources. Additionally, We propose a quantum information scrambling protocol, where a specific node scrambles secret quantum information across the entire network. This protocol ensures that a malicious party would need access to a significant subset of the network to retrieve the information.