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.
 R. Penrose, in Combinatorial Mathematics and its Applications, edited by D. Welsh (Academic Press, New York, 1971) pp. 221–244.
 P. Selinger, ``A Survey of Graphical Languages for Monoidal Categories,'' in New Structures for Physics (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011) pp. 289–355.
 B. Coecke and S. Perdrix, in Computer Science Logic: 24th International Workshop, CSL 2010, 19th Annual Conference of the EACSL, Brno, Czech Republic, August 23-27, 2010. Proceedings (Springer Berlin Heidelberg, Berlin, Heidelberg, 2010) pp. 230–244,.
 B. Coecke, Q. Wang, B. Wang, Y. Wang, and Q. Zhang, in Proceedings of the 6th International Workshop on Quantum Physics and Logic (QPL 2009) (2011) pp. 231 – 249.
 U. Maurer and R. Renner, in Innovations in Computer Science (Tsinghua University Press, 2011) pp. 1–21.
 D. Pavlovic, in Categories and Types in Logic, Language, and Physics - Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday, Vol. 8222 (2014).
 M. Stay and J. Vicary, Electronic Notes in Theoretical Computer Science 298, 367 (2013), proceedings of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX.
 P. Bierhorst, E. Knill, S. Glancy, A. Mink, S. Jordan, A. Rommal, Y.-K. Liu, B. Christensen, S. W. Nam, and L. K. Shalm, ``Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling,'' (2017).
 M. Coudron and H. Yuen, in Proceedings of the Forty-sixth Annual ACM Symposium on Theory of Computing, STOC '14 (ACM, New York, NY, USA, 2014) pp. 427–436.
 S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A Manning, and C. Monroe, Nature 464, 1021 (2010).
 National Institute of Standards and Technology (NIST), ``Randomness Beacon Program,'' https://www.nist.gov/programs-projects/nist-randomness-beacon, accessed: 2019-02-01.
 U. Vazirani and T. Vidick, in Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing, STOC '12 (ACM, New York, NY, USA, 2012) pp. 61–76.
 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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