Characterising the correlations of prepare-and-measure quantum networks

TL;DR

This paper introduces a computational toolbox for efficiently characterizing the correlations in prepare-and-measure quantum networks, which are essential for quantum communication and cryptography, using only the inner-product information of quantum encodings.

Contribution

The authors develop a versatile, efficient method to analyze input-output distributions in P&M quantum networks, including those with infinite-dimensional states, advancing quantum network analysis.

Findings

Revealed new results in multipartite quantum distributed computing

Demonstrated the toolbox's effectiveness in quantum cryptography

Potential implications for quantum network information theory

Abstract

Prepare-and-measure (P&M) quantum networks are the basic building blocks of quantum communication and cryptography. These networks crucially rely on non-orthogonal quantum encodings to distribute quantum correlations, thus enabling superior communication rates and information-theoretic security. Here, we present a computational toolbox that is able to efficiently characterise the set of input-output probability distributions for any discrete-variable P&M quantum network, assuming only the inner-product information of the quantum encodings. Our toolbox is thus highly versatile and can be used to analyse a wide range of quantum network protocols, including those that employ infinite-dimensional quantum code 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 implications for quantum network information theory and the development of new quantum technologies.