Graphical Methods in Device-Independent Quantum Cryptography

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.

Publishable version. Diagrams have been polished, minor revisions to the text, and an appendix added with supplementary proofs

References in corpus (3)

• Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals
• Simple and tight device-independent security proofs
• Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus

Cited by in corpus (1)

• Categorical composable cryptography