References

  1. S. Abramsky & B. Coecke (2004): A categorical semantics of quantum protocols. In: Logic in Computer Science. IEEE Computer Society, pp. 415–425, doi:10.1109/LICS.2004.1.
  2. J. Adamek, H. Herrlich & G. Strecker (2006): Abstract and concrete categories: the joy of cats. Reprint 17. Theory and Applications of Categories.
  3. G. Chiribella (2014): Dilation of states and processes in operational-probabilistic theories. In: Quantum Physics and Logic, EPTCS 172, pp. 1–14, doi:10.4204/EPTCS.172.1.
  4. G. Chiribella (2014): Distinguishability and copiability of programs in general process theories. International Journal of Software and Informatics 8(3–4), pp. 209–223. Available at http://arxiv.org/abs/1411.3035.
  5. G. Chiribella, G. M. D'Ariano & P. Perinotti (2010): Probabilistic theories with purification. Physical Review A 81, pp. 062348, doi:10.1103/PhysRevA.81.062348.
  6. G. Chiribella & C. M. Scandolo (2015): Operational axioms for diagonalizing states. In: Quantum Physics and Logic, EPTCS 195, pp. 96–115, doi:10.4204/EPTCS.195.8.
  7. M.-D. Choi (1975): Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, pp. 285–290, doi:10.1016/0024-3795(75)90075-0.
  8. B. Coecke & C. Heunen (2016): Pictures of complete positivity in arbitrary dimension. Information and Computation 250, pp. 50–58, doi:10.1016/j.ic.2016.02.007.
  9. B. Coecke & A. Kissinger (2017): Picturing quantum processes: a first course in quantum theory and diagrammatic reasoning. Cambridge University Press, doi:10.1017/9781316219317.
  10. B. Coecke & S. Perdrix (2010): Environment and classical channels in categorical quantum mechanics. Logical Methods in Computer Science 8(4), pp. 14, doi:10.2168/LMCS-8(4:14)2012.
  11. O. Cunningham & C. Heunen (2015): Axiomatizing complete positivity. In: Quantum Physics and Logic, EPTCS 195, pp. 148–157, doi:10.4204/EPTCS.195.11.
  12. P. Freyd & G. M. Kelly (1972): Categories of continuous functors I. Journal of Pure and Applied Algebra 2, pp. 169–191, doi:10.1016/0022-4049(72)90001-1.
  13. C. Heunen & J. Vicary (2017): Categories for quantum theory: an introduction. Oxford University Press.
  14. A. Joyal (2008): The theory of quasi-categories and its applications. Quaderns 45, pp. 149–496. Available at http://mat.uab.cat/~kock/crm/hocat/advanced-course/Quadern45-2.pdf.
  15. J. Selby & B. Coecke (2017): Leaks: quantum, classical, intermediate, and more. Entropy 19(4), pp. 174, doi:10.3390/e19040174.
  16. P. Selinger (2007): Dagger compact closed categories and completely positive maps. In: Quantum Physics and Logic, ENTCS 170, pp. 139–163, doi:10.1016/j.entcs.2006.12.018.
  17. P. Selinger (2009): A survey of graphical languages for monoidal categories. In: New Structures for Physics, Lecture Notes in Physics. Springer, pp. 289–355, doi:10.1007/978-3-642-12821-9_4.
  18. W. F. Stinespring (1955): Positive functions on C*-algebras. Proceedings of the American Mathematical Society 6, pp. 211–216, doi:10.2307/2032342.
  19. A. Westerbaan & B. Westerbaan (2016): Paschke dilations. In: Quantum Physics and Logic, EPTCS 236, pp. 229–244, doi:10.4204/EPTCS.236.15.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org