S. Abramsky & B. Coecke (2004):
A categorical semantics of quantum protocols.
In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS),
pp. 415–425,
doi:10.1109/LICS.2004.1319636.
arXiv:quant-ph/0402130.
A. Asperti & G. Longo (1991):
Categories, types, and structures: an introduction to category theory for the working computer scientist.
MIT press.
H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa & B. Schumacher (1996):
Noncommuting mixed states cannot be broadcast.
Physical Review Letters 76,
pp. 2818,
doi:10.1103/PhysRevLett.76.2818.
R. Blume-Kohout, H. K. Ng, D. Poulin & L. Viola (2010):
Information-preserving structures: A general framework for quantum zero-error information.
Physical Review A 82(6),
pp. 062306,
doi:10.1103/PhysRevA.82.062306.
F. Borceux & D. Dejean (1986):
Cauchy completion in category theory.
Cahiers de topologie et géométrie différentielle catégoriques 27(2),
pp. 133–146.
O. Bratteli (1972):
Inductive limits of finite dimensional C*-algebras.
Transactions of the American Mathematical Society 171,
pp. 195–234,
doi:10.2307/1996380.
G. Chiribella, G. M. D'Ariano & P. Perinotti (2010):
Probabilistic theories with purification.
Physical Review A 81(6),
pp. 062348,
doi:10.1103/PhysRevA.81.062348.
G. Chiribella, G. M. D'Ariano & P. Perinotti (2011):
Informational derivation of quantum theory.
Physical Review A 84(1),
pp. 012311,
doi:10.1103/PhysRevA.84.012311.
K. Cho, B. Jacobs, B. Westerbaan & A. Westerbaan (2015):
An introduction to effectus theory.
arXiv:1512.05813.
B. Coecke (2008):
Axiomatic description of mixed states from Selinger's CPM-construction.
Electronic Notes in Theoretical Computer Science 210,
pp. 3–13,
doi:10.1016/j.entcs.2008.04.014.
B. Coecke (2014):
Terminality implies non-signalling,
doi:10.4204/EPTCS.172.3.
ArXiv:1405.3681.
B. Coecke & A. Kissinger (2016):
Categorical quantum mechanics I: causal quantum processes.
In: E. Landry: Categories for the Working Philosopher.
Oxford University Press.
ArXiv:1510.05468.
B. Coecke & A. Kissinger (2016):
Picturing Quantum Processes. A First Course in Quantum Theory and Diagrammatic Reasoning.
Cambridge University Press,
doi:10.1017/9781316219317.
B. Coecke & S. Perdrix (2010):
Environment and classical channels in categorical quantum mechanics.
In: Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL),
Lecture Notes in Computer Science 6247,
pp. 230–244,
doi:10.1007/978-3-642-15205-4_20.
Extended version: arXiv:1004.1598.
H. Cohn (2004):
Projective geometry over F_1 and the Gaussian binomial coefficients.
The American Mathematical Monthly 111(6),
pp. 487–495,
doi:10.2307/4145067.
O. Cunningham & C. Heunen (2015):
Axiomatizing complete positivity.
arXiv preprint arXiv:1506.02931,
doi:10.4204/EPTCS.195.11.
R. DeMarr (1974):
Nonnegative idempotent matrices.
Proceedings of the American Mathematical Society 45(2),
pp. 185–188,
doi:10.1090/S0002-9939-1974-0354738-X.
P. Flor (1969):
On groups of non-negative matrices.
Compositio Mathematica 21(4),
pp. 376–382.
L. Hardy & W. K. Wootters (2012):
Limited holism and real-vector-space quantum theory.
Foundations of Physics 42(3),
pp. 454–473,
doi:10.1007/s10701-011-9616-6.
C. Heunen, A. Kissinger & P. Selinger (2014):
Completely positive projections and biproducts.
In: Bob Coecke & Matty Hoban: Proceedings of the 10th International Workshop on Quantum Physics and Logic,
Electronic Proceedings in Theoretical Computer Science 171.
Open Publishing Association,
pp. 71–83,
doi:10.4204/EPTCS.171.7.
J. Lambek & P. J. Scott (1988):
Introduction to Higher-order Categorical Logic.
Cambridge University Press.
S. Mac Lane (1998):
Categories for the working mathematician.
Springer-verlag,
doi:10.1007/978-1-4757-4721-8.
L. Masanes, M. P. Müller, R. Augusiak & D. Pérez-García (2013):
Existence of an information unit as a postulate of quantum theory.
Proceedings of the National Academy of Sciences 110(41),
pp. 16373–16377,
doi:10.1073/pnas.1304884110.
B. Schumacher & M. D. Westmoreland (2012):
Modal quantum theory.
Foundations of Physics 42(7),
pp. 918–925,
doi:10.1007/s10701-012-9650-z.
B. Schumacher & M. D. Westmoreland (2016):
Almost quantum theory.
In: Quantum Theory: Informational Foundations and Foils.
Springer,
pp. 45–81,
doi:10.1007/978-94-017-7303-4_3.
John Selby & Bob Coecke (2017):
Leaks: quantum, classical, intermediate and more.
Entropy 19(4),
pp. 174,
doi:10.3390/e19040174.
P. Selinger (2007):
Dagger compact closed categories and completely positive maps.
Electronic Notes in Theoretical Computer Science 170,
pp. 139–163,
doi:10.1016/j.entcs.2006.12.018.
P. Selinger (2008):
Idempotents in Dagger Categories (Extended Abstract).
Electronic Notes in Theoretical Computer Science 210,
pp. 107–122,
doi:10.1016/j.entcs.2008.04.021.
J. Vicary (2011):
Categorical formulation of finite-dimensional quantum algebras.
Communications in Mathematical Physics 304(3),
pp. 765–796,
doi:10.1007/s00220-010-1138-0.