Bob Coecke
Chief Scientist at Quantinuum
On quantum protocols in quantum information theory (such as quantum teleportation) formalized as string diagrams in the dagger-compact category of finite-dimensional Hilbert spaces (quantum information theory via dagger-compact categories):
Samson Abramsky, Bob Coecke, A categorical semantics of quantum protocols , Proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS’04). IEEE Computer Science Press (2004) [arXiv:quant-ph/0402130]
Samson Abramsky, Bob Coecke, Abstract Physical Traces, Theory and Applications of Categories, 14 6 (2005) 111-124. [tac:14-06, arXiv:0910.3144]
Bob Coecke, De-linearizing Linearity: Projective Quantum Axiomatics from Strong Compact Closure, Proceedings of the 3rd International Workshop on Quantum Programming Languages (2005), Electronic Notes in Theoretical Computer Science 170 (2007) 49-72 [doi:10.1016/j.entcs.2006.12.011, arXiv:quant-ph/0506134]
Samson Abramsky, Bob Coecke, Categorical quantum mechanics, in Handbook of Quantum Logic and Quantum Structures, Elsevier (2008) [arXiv:0808.1023, ISBN:9780080931661, doi:10.1109/LICS.2004.1319636]
Survey in contrast to quantum logic:
More on the use of string diagrams in quantum information theory via dagger-compact categories:
Bob Coecke, Kindergarten quantum mechanics (arXiv:quant-ph/0510032)
Bob Coecke, Quantum Picturalism, Contemporary Physics 51 1 (2010) [arXiv:0908.1787, doi:10.1080/00107510903257624]
Bob Coecke, Ross Duncan, Interacting Quantum Observables: Categorical Algebra and Diagrammatics, New J. Phys. 13 (2011) 043016 arXiv:0906.4725, doi:10.1088/1367-2630/13/4/043016
Textbook accounts:
Bob Coecke, Aleks Kissinger, Picturing Quantum Processes – A First Course in Quantum Theory and Diagrammatic Reasoning, Cambridge University Press (2017) [ISBN:9781107104228]
Bob Coecke, Stefano Gogioso, Quantum in Pictures, Quantinuum Publications (2023) [ISBN 978-1739214715, Quantinuum blog]
(including the ZX-calculus)
Motivation and introduction basic concepts of category theory for an audience familiar with standard physics and in particular with quantum mechanics (see also higher category theory and physics):
Bob Coecke, Introducing categories to the practicing physicist (arXiv:0808.1032)
Bob Coecke, Eric Oliver Paquette, Categories for the practising physicist, in: New Structures for Physics, Lecture Notes in Physics 813, Springer (2010) [arXiv:0905.3010, doi:10.1007/978-3-642-12821-9_3]
The article focuses towards the end on monoidal categories, their description in terms of string diagrams and on quantum mechanics in terms of dagger-compact categories.
On quantum measurement formulated in finite quantum mechanics in terms of dagger-compact categories in terms of Frobenius algebras and the quantum reader monad:
Bob Coecke, Duško Pavlović, Quantum measurements without sums, in Louis Kauffman, Samuel Lomonaco (eds.), Mathematics of Quantum Computation and Quantum Technology, Taylor & Francis (2008) 559-596 [arXiv:quant-ph/0608035, doi:10.1201/9781584889007]
Bob Coecke, Eric Oliver Paquette, POVMs and Naimark’s theorem without sums, Electronic Notes in Theoretical Computer Science 210 (2008) 15-31 [arXiv:quant-ph/0608072, doi:10.1016/j.entcs.2008.04.015]
Bob Coecke, Eric Paquette, Dusko Pavlovic, Classical and quantum structures (2008) [pdf, pdf]
Bob Coecke, Eric Oliver Paquette, Duško Pavlović, Classical and quantum structuralism [arXiv:0904.1997]
Bob Coecke, Duško Pavlović, Jamie Vicary, A new description of orthogonal bases, Mathematical Structures in Computer Science 23 3 (2012) 555- 567 [arXiv:0810.0812, doi:10.1017/S0960129512000047]
Introducting the ZX-calculus:
Bob Coecke, Ross Duncan, A graphical calculus for quantum observables [pdf]
Bob Coecke, Ross Duncan, Interacting Quantum Observables, in Automata, Languages and Programming. ICALP 2008, Lecture Notes in Computer Science 5126, Springer (2008) [doi:10.1007/978-3-540-70583-3_25]
Bob Coecke, Ross Duncan, Interacting Quantum Observables: Categorical Algebra and Diagrammatics, New J. Phys. 13 (2011) 043016 [arXiv:0906.4725, doi:10.1088/1367-2630/13/4/043016]
Bob Coecke, Basic ZX-calculus for students and professionals [arXiv:2303.03163]
Discussion of DisCoPy:
Last revised on November 6, 2023 at 16:56:27. See the history of this page for a list of all contributions to it.