# Graphical Methods in Device-Independent Quantum Cryptography

Spencer Breiner1, Carl A. Miller1,2, and Neil J. Ross2,3

1National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, USA
2Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, MD 20742, USA
3Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 4R2, Canada

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### Abstract

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this result, and implement part of it in the Globular proof assistant.

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### Cited by

[1] Spencer Breiner, Amir Kalev, and Carl A. Miller, "Parallel Self-Testing of the GHZ State with a Proof by Diagrams", arXiv:1806.04744.

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