References

  1. S. Abramsky & B. Coecke (2004): A categorical semantics of quantum protocols. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004. IEEE, pp. 415–425, doi:10.1109/LICS.2004.1319636.
  2. Samson Abramsky & Chris Heunen (2012): H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics. Mathematical Foundations of Information Flow 71, pp. 1–24, doi:10.1090/psapm/071/599.
  3. Miriam Backens (2014): The ZX-calculus is complete for stabilizer quantum mechanics. New Journal of Physics 16(9), doi:10.1088/1367-2630/16/9/093021.
  4. Bob Coecke (2009): Quantum Picturalism. Contemporary Physics, doi:10.1080/00107510903257624.
  5. Bob Coecke & Ross Duncan (2011): Interacting quantum observables: Categorical algebra and diagrammatics. New Journal of Physics 13, doi:10.1088/1367-2630/13/4/043016.
  6. Bob Coecke, Chris Heunen & Aleks Kissinger (2014): Categories of quantum and classical channels. Quantum Information Processing, pp. 1–31, doi:10.1007/s11128-014-0837-4.
  7. Bob Coecke & Aleks Kissinger (2017): Picturing Quantum Processes. Cambridge University Press, doi:10.1017/9781316219317.
  8. Bob Coecke & Dusko Pavlovic (2007): Quantum measurements without sums. In: Mathematics of Quantum Computation and Quantum Technology, pp. 559–596, doi:10.1201/9781584889007.ch16.
  9. Bob Coecke, Dusko Pavlovic & Jamie Vicary (2013): A new description of orthogonal bases. Mathematical Structures in Computer Science 23(03), doi:10.1017/S0960129512000047.
  10. M. O. Farrukh (1975): Application of nonstandard analysis to quantum mechanics. Journal of Mathematical Physics 16(2), doi:10.1063/1.522525.
  11. Stefano Gogioso & Fabrizio Genovese (2016): Infinite-dimensional Categorical Quantum Mechanics, doi:10.4204/EPTCS.236.4.
  12. Stefano Gogioso & Aleks Kissinger (2017): Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem.
  13. Stefano Gogioso & William Zeng (2017): Generalised Mermin-type non-locality arguments.
  14. André Joyal & Ross Street (1991): The Geometry of Tensor Calculus I. Advances in Mathematics 88, pp. 55–112, doi:10.1016/0001-8708(91)90003-P.
  15. André Joyal, Ross Street & Dominic Verity (1996): Traced Monoidal Categories. Mathematical Proceedings of the Cambridge Philosophical Society 119(03), pp. 447–468, doi:10.1017/S0305004100074338.
  16. Gottfried Wilhelm Leibniz (1684): Nova methodus pro maximis et minimis itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus. Acta Eruditorum.
  17. John von Neumann (1939): On infinite direct products. Compositio Mathematica 6.
  18. John von Neumann (1949): On Rings of Operators. Reduction Theory. The Annals of Mathematics 50(2), pp. 401–486, doi:10.2307/1969463.
  19. Izumi Ojima & Masanao Ozawa (1993): Unitary representations of the hyperfinite Heisenberg group and the logical extension methods in physics. Open Systems & Information Dynamics 2(1), pp. 107–128, doi:10.1007/BF02228975.
  20. Masanao Ozawa (1989): Realization of Measurement and the Standard Quantum Limit. In: P. Tombesi & R. Pike: Squeezed and Nonclassical Light, pp. 263–286, doi:10.1007/978-1-4757-6574-8_20.
  21. Masanao Ozawa (1997): Phase Operator Problem and Macroscopic Extension of Quantum Mechanics. Annals of Physics 257(1), pp. 65–83, doi:10.1006/aphy.1997.5685.
  22. Andreas Raab (2006): An approach to nonstandard quantum mechanics, doi:10.1063/1.1812358.
  23. Abraham Robinson (1974): Non-standard analysis. Princeton University Press, doi:10.1515/9781400884223.
  24. Peter Selinger (2009): A survey of graphical languages for monoidal categories. Lecture Notes in Physics 813, pp. 289–355, doi:10.1007/978-3-642-12821-9_4.
  25. Dominic Verdon & Jamie Vicary (2017): Tight Reference Frame–Independent Quantum Teleportation. Electronic Proceedings in Theoretical Computer Science 236, pp. 202–214, doi:10.4204/EPTCS.236.13.
  26. Hideyasu Yamashita & Masanao Ozawa (2000): Nonstandard representations of the canonical commutation relations. Reviews in Mathematical Physics 12(11), pp. 1407–1427, doi:10.1142/S0129055X00000617.

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