Characterising the correlations of prepare-and-measure quantum networks

Abstract

It is well known that transmitting classical information over quantum networks can significantly improve communication rates and achieve secure communication. These quantum advantages crucially rely on the network's innate ability to distribute classical correlations reliably and securely. To this end, 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. Taken together, these findings suggest that our method may have important implications for quantum network information theory and the development of new quantum technologies.