Samson Abramsky
2012
Big toy models - Representing physical systems as Chu spaces
Synthese
186
3
697–718
10.1007/s11229-011-9912-x
Samson Abramsky
Bob Coecke
2004
A Categorical Semantics of Quantum Protocols
Proceedings of LICS 2004
IEEE Computer Society
415–425
10.1109/LICS.2004.1
Jiři Adámek
Jiři Rosický
1994
Locally Presentable and Accessible Categories
London Mathematical Society Lecture Notes
189
Cambridge University Press
10.1017/CBO9780511600579
Enrico G. Beltrametti
Slawomir Bugajski
1997
Effect algebras and statistical physical theories
Journal of Mathematical Physics
38
3020–3030
10.1063/1.532031
Garrett Birkhoff
John von Neumann
1936
The logic of quantum mechanics
Annals of Mathematics
37
823–843
10.2307/1968621
Aurelio Carboni
Robert F.C. Walters
1987
Cartesian bicategories, I
J. of Pure and Applied Algebra
49
11–32
10.1016/0022-4049(87)90121-6
Kenta Cho
Bart Jacobs
Bas Westerbaan
Abraham Westerbaan
2015
An Introduction to Effectus Theory
http://arxiv.org/abs/1512.05813
Bob Coecke
Ross Duncan
2011
Interacting quantum observables: categorical algebra and diagrammatics
New Journal of Physics
13
4
80pp
10.1088/1367-2630/13/4/043016
Arxiv:0906.4725
Bob Coecke
Chris Heunen
Aleks Kissinger
2013
Compositional quantum logic
Bob Coecke
Luke Ong
Prakash Panangaden
Computation, Logic, Games, and Quantum Foundations
21–36
10.1007/978-3-642-38164-5_3
Bob Coecke
Aleks Kissinger
2010
The Compositional Structure of Multipartite Quantum Entanglement
Proceedings of ICALP 2010, Part II
297–308
10.1007/978-3-642-14162-1_25
Bob Coecke
Aleks Kissinger
Alex Merry
Shibdas Roy
2010
The GHZ/W-calculus contains rational arithmetic
Farid M. Ablayev
Bob Coecke
Alexander Vasiliev
CSR Workshop on High Productivity Computations, HPC 2010
EPTCS
52
34–48
Bob Coecke
Éric Oliver Paquette
Dusko Pavlovic
2009
Classical and quantum structuralism
Simon Gay
Ian Mackie
Semantical Techniques in Quantum Computation
Cambridge University Press
29–69
10.1017/CBO9781139193313.003
Bob Coecke
Dusko Pavlovic
2007
Quantum measurements without sums
G. Chen
L. Kauffman
S. Lamonaco
Mathematics of Quantum Computing and Technology
Taylor and Francis
36pp
10.1201/9781584889007.ch16
http://arxiv.org/abs/quant-ph/0608035
Bob Coecke
Dusko Pavlovic
Jamie Vicary
2013
A new description of orthogonal bases
Math. Structures in Comp. Sci.
23
3
555–567
10.1017/S0960129512000047
http://arxiv.org/abs/0810.0812
David J Foulis
Mary Katherine Bennett
1994
Effect algebras and unsharp quantum logics
Foundations of Physics
24
10
1331–1352
10.1007/BF02283036
Peter Freyd
Andre Scedrov
1990
Categories, Allegories
Mathematical Library
39
North-Holland
Stefano Gogioso
2015
A Bestiary of Sets and Relations
Chris Heunen
Peter Selinger
Jamie Vicary
Proceedings QPL 2015
Electronic Proceedings in Theoretical Computer Science
195
Open Publishing Association
208–227
10.4204/EPTCS.195.16
Stanley Gudder
1997
Effect test spaces and effect algebras
Foundations of Physics
27
2
287–304
10.1007/BF02550455
Amar Hadzihasanovic
2015
A Diagrammatic Axiomatisation for Qubit Entanglement
Symposium on Logic in Computer Science (LICS) 2015
IEEE Computer Society
573–584
10.1109/LICS.2015.59
Chris Heunen
Sean Tull
2015
Categories of relations as models of quantum theory
Chris Heunen
Peter Selinger
Jamie Vicary
Proceedings of QPL 2015
Electronic Proceedings in Theoretical Computer Science
195
Open Publishing Association
247–261
10.4204/EPTCS.195.18
Bart Jacobs
2015
New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic
Logical Methods in Computer Science
11
3
10.2168/LMCS-11(3:24)2015
G. Max Kelly
Manuel L. Laplaza
1980
Coherence for compact closed categories
Journal of Pure and Applied Algebra
19
193 – 213
10.1016/0022-4049(80)90101-2
N. David Mermin
1985
Is the moon there when nobody looks? Reality and the quantum theory
Physics Today
38–47
10.1063/1.880968
Robin Milner
1977
Fully abstract models of typed λ-calculi
Theoretical Computer Science
4
1
1 – 22
10.1016/0304-3975(77)90053-6
John von Neumann
1955
Mathematical Foundations of Quantum Mechanics
Investigations in physics
Princeton University Press
John von Neumann
1960
Continuous Geometry
Princeton Landmarks in Mathematics and Physics
Princeton University Press
Dusko Pavlovic
1995
Maps I: relative to a factorisation system
J. Pure Appl. Algebra
99
9–34
10.1016/0022-4049(94)00054-M
Dusko Pavlovic
1996
Maps II: Chasing diagrams in categorical proof theory
J. of the IGPL
4
2
1–36
10.1093/jigpal/4.2.159
Dusko Pavlovic
2009
Quantum and classical structures in nondeterministic computation
Peter Bruza
Don Sofge
Keith van Rijsbergen
Proceedings of Quantum Interaction 2009
Lecture Notes in Artificial Intelligence
5494
Springer Verlag
143–158
10.1007/978-3-642-00834-4_13
http://arxiv.org/abs/0812.2266
Dusko Pavlovic
2011
Relating toy models of quantum computation: comprehension, complementarity and dagger autonomous categories
E. Notes in Theor. Comp. Sci.
270
2
121–139
10.1016/j.entcs.2011.01.027
http://arxiv.org/abs/1006.1011
Dusko Pavlovic
2012
Geometry of abstraction in quantum computation
Proceedings of Symposia in Applied Mathematics
71
233–267
10.1090/psapm/071/607
http://arxiv.org/abs/1006.1010
C. H. Randall
D. J. Foulis
1970
An Approach to Empirical Logic
The American Mathematical Monthly
77
4
363–374
10.2307/2316143
Miklós Rédei
1996
Why John von Neumann did not like the Hilbert Space formalism of quantum mechanics (and what he liked instead)
Studies in History and Philosophy of Modern Physics
27
4
493–510
10.1016/S1355-2198(96)00017-2
Peter Selinger
2007
Dagger Compact Closed Categories and Completely Positive Maps
Electron. Notes Theor. Comput. Sci.
170
139–163
10.1016/j.entcs.2006.12.018
Robert W. Spekkens
2007
In defense of the epistemic view of quantum states: a toy theory
Physical Review A
75
032110
10.1103/PhysRevA.75.032110