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author = {Erik M. Alfsen},
year = {1971},
title = {{Compact Convex Sets and Boundary Integrals}},
series = {Ergebnisse der Mathematik und ihrer Grenzgebiete},
publisher = {Springer},
doi = {10.1007/978-3-642-65009-3},
)
@book(alfsen01,
author = {Erik M. Alfsen and Frederic W. Shultz},
year = {2001},
title = {{State Spaces of Operator Algebras}},
publisher = {Birkh\"auser},
doi = {10.1007/978-1-4612-0147-2},
)
@book(asimow,
author = {Leonard Asimow and Alan J. Ellis},
year = {1980},
title = {{Convexity Theory and its Applications in Functional Analysis}},
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@article(barnum2010,
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year = {2010},
title = {Entropy and information causality in general probabilistic theories},
journal = {New Journal of Physics},
volume = {12},
number = {3},
pages = {033024},
doi = {10.1088/1367-2630/12/3/033024},
)
@misc(barnum,
author = {Howard Barnum and Alexander Wilce},
year = {2009},
title = {{Ordered Linear Spaces and Categories as Frameworks for Information-Processing Characterizations of Quantum and Classical Theory}},
howpublished = {\url{http://arxiv.org/abs/0908.2354}},
)
@article(barrett07,
author = {Jonathan Barrett},
year = {2007},
title = {{Information Processing in Generalized Probabilistic Theories}},
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doi = {10.1103/PhysRevA.75.032304},
)
@article(beltrametti,
author = {Enrico G. Beltrametti and S{\l}awomir Bugajski},
year = {1997},
title = {{Effect Algebras and Statistical Physical Theories}},
journal = {Journal of Mathematical Physics},
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number = {6},
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)
@book(bourbaki,
author = {Nicolas Bourbaki},
year = {1998},
title = {{General Topology}},
series = {Ettore Majorana International Science},
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@article(chiribella2010,
author = {Giulio Chiribella and Giacomo Mauro D'Ariano and Paolo Perinotti},
year = {2010},
title = {{Probabilistic Theories with Purification}},
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@article(davies,
author = {E. Brian Davies and John T. Lewis},
year = {1970},
title = {{An Operational Approach to Quantum Probability}},
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url = {http://projecteuclid.org/euclid.cmp/1103842336},
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@book(DvurecenskijP00,
author = {Dvure\v{c}enskij, Anatolij and Sylvia Pulmannov{\'a}},
year = {2000},
title = {New Trends in Quantum Structures},
publisher = {Kluwer Acad. Publ.},
address = {Dordrecht},
doi = {10.1007/978-94-017-2422-7},
)
@article(edwards,
author = {Christopher M. Edwards},
year = {1970},
title = {{The Operational Approach to Algebraic Quantum Theory I}},
journal = {Communications in Mathematical Physics},
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doi = {10.1007/BF01646788},
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author = {Alan J. Ellis},
year = {1964},
title = {{The Duality of Partially Ordered Normed Linear Spaces}},
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url = {http://jlms.oxfordjournals.org/content/s1-39/1/730.short},
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author = {David J. Foulis and Mary K. Bennett},
year = {1994},
title = {{Effect Algebras and Unsharp Quantum Logics}},
journal = {Foundations of Physics},
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pages = {1331--1352},
doi = {10.1007/BF02283036},
)
@misc(Fritz09a,
author = {Tobias Fritz},
year = {2009},
title = {{Convex Spaces I: Definition and Examples}},
howpublished = {\url{https://arxiv.org/abs/0903.5522}},
)
@phdthesis(furberthesis,
author = {Robert Furber},
year = {2017},
title = {{Categorical Duality in Probability and Quantum Foundations}},
school = {Radboud Universiteit Nijmegen},
note = {Link available at \url{http://www.robertfurber.com}},
)
@article(Gudder1973,
author = {Stanley Gudder},
year = {1973},
title = {{Convex Structures and Operational Quantum Mechanics}},
journal = {Communications in Mathematical Physics},
volume = {29},
number = {3},
pages = {249--264},
doi = {10.1007/BF01645250},
)
@article(PulmannovaG98,
author = {Stanley Gudder and Sylvia Pulmannov\'a},
year = {1998},
title = {{Representation Theorem for Convex Effect Algebras}},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {39},
number = {4},
pages = {645 -- 659},
)
@book(olsen,
author = {Hanche-Olsen, Harald and St{\o}rmer, Erling},
year = {1984},
title = {{Jordan Operator Algebras}},
publisher = {Pitman Publishing},
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@incollection(Jacobs10e,
author = {Bart Jacobs},
year = {2010},
title = {{Convexity, Duality and Effects}},
editor = {Cristian S. Calude and Vladimiro Sassone},
booktitle = {Theoretical Computer Science},
series = {IFIP Advances in Information and Communication Technology},
volume = {323},
publisher = {Springer Berlin Heidelberg},
pages = {1--19},
doi = {10.1007/978-3-642-15240-5_1},
)
@inproceedings(JacobsM12b,
author = {Bart Jacobs and Jorik Mandemaker},
year = {2012},
title = {{The Expectation Monad in Quantum Foundations}},
editor = {Bart Jacobs and Peter Selinger and Bas Spitters},
booktitle = {Quantum Physics and Logic (QPL) 2011},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {95},
pages = {143--182},
doi = {10.4204/EPTCS.95.12},
)
@book(jameson,
author = {Graham Jameson},
year = {1970},
title = {{Ordered Linear Spaces}},
series = {Lecture Notes in Mathematics},
volume = {141},
publisher = {Springer},
doi = {10.1007/BFb0059130},
)
@book(johnstone,
author = {Peter Johnstone},
year = {1982},
title = {{Stone Spaces}},
series = {Cambridge Studies in Advanced Mathematics},
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publisher = {Cambridge University Press},
)
@article(jordan,
author = {Pascual Jordan and John von Neumann and Eugene Wigner},
year = {1934},
title = {{On an Algebraic Generalization of the Quantum Mechanical Formalism}},
journal = {Annals of Mathematics},
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number = {1},
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doi = {10.2307/1968117},
)
@book(lambek,
author = {Joachim Lambek and Philip Scott},
year = {1986},
title = {{Introduction to Higher Order Categorical Logic}},
series = {Cambridge Studies in Advanced Mathematics},
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publisher = {Cambridge University Press},
)
@book(maclane,
author = {Mac Lane, Saunders},
year = {1971},
title = {{Categories for the Working Mathematician}},
series = {Graduate Texts in Mathematics},
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@article(Neumann1970,
author = {Walter D. Neumann},
year = {1970},
title = {{On the Quasivariety of Convex Subsets of Affine Spaces}},
journal = {Archiv der Mathematik},
volume = {21},
number = {1},
pages = {11--16},
doi = {10.1007/BF01220869},
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@article(ozawa80,
author = {Masanao Ozawa},
year = {1980},
title = {{Optimal Measurements for General Quantum Systems}},
journal = {Reports on Mathematical Physics},
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@article(pumplun02,
author = {Dieter Pumpl\"un},
year = {2002},
title = {{The Metric Completion of Convex Sets and Modules}},
journal = {Results in Mathematics},
volume = {41},
number = {3-4},
pages = {346--360},
doi = {10.1007/BF03322777},
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@phdthesis(roumenthesis,
author = {Frank Roumen},
year = {2017},
title = {{Effect Algebroids}},
school = {Radboud Universiteit Nijmegen},
)
@book(schaefer,
author = {Helmut H. Schaefer},
year = {1966},
title = {{Topological Vector Spaces}},
series = {Graduate Texts in Mathematics},
volume = {3},
publisher = {Springer Verlag},
)
@article(shultz74,
author = {Frederic W. Shultz},
year = {1974},
title = {{A Characterization of State Spaces of Orthomodular Lattices}},
journal = {Journal of Combinatorial Theory, Series A},
volume = {17},
number = {3},
pages = {317 -- 328},
doi = {10.1016/0097-3165(74)90096-X},
)
@article(Stone1949,
author = {Marshall H. Stone},
year = {1949},
title = {{Postulates for the Barycentric Calculus}},
journal = {Annali di Matematica Pura ed Applicata},
volume = {29},
number = {1},
pages = {25--30},
doi = {10.1007/BF02413910},
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@misc(swirszcz75,
author = {Tadeusz \'Swirszcz},
year = {1975},
title = {{Monadic Functors and Categories of Convex Sets}},
howpublished = {Institute of Mathematics of the Polish Academy of Sciences, Preprint 70},
)