It is well known that transmitting classical
information over quantum networks can significantly improve
communication rates and provide secure communication. These quantum
advantages crucially rely on the network's innate ability to distribute
classical correlations reliably and securely. Hence it is of significant
interest to understand how classical information propagates in quantum
networks. Here, we report a computational toolbox that is able to
characterise the stochastic matrix of any classical-quantum network,
assuming only the inner-product information of the quantum code states.
The toolbox is hence highly versatile and can analyse a wide range of
quantum network protocols, including those that employ
infinite-dimensional quantum states. To demonstrate the feasibility and
efficacy of our toolbox, we use it to reveal new results in multipartite
quantum distributed computing and quantum cryptography.
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