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@article{moore1900,
title={A Simple Proof of the Fundamental {C}auchy--{G}oursat Theorem},
author={Moore, Eliakim H.},
journal={Transactions of the American Mathematical Society},
volume={1},
number={4},
pages={499--506},
year={1900},
note={\doi{10.1090/S0002-9947-1900-1500551-3}}
}
@article{cho2016semantics,
title={Semantics for a quantum programming language by operator algebras},
author={Cho, Kenta},
journal={New Generation Computing},
volume={34},
number={1-2},
pages={25--68},
year={2016},
publisher={Springer},
note={\doi{10.1007/s00354-016-0204-3}}
}
@article{jacobs2013block,
title={On block structures in quantum computation},
author={Jacobs, Bart P.F.},
journal={ENTCS},
volume={298},
pages={233--255},
year={2013},
note={\doi{10.1016/j.entcs.2013.09.016}}
}
@mastersthesis{rennela2015operator,
title={Operator Algebras in Quantum Computation},
author={Rennela, Mathys P.A.},
note={\arXiv{1510.06649v1}},
school={Radboud University},
year={2015}
}
@inproceedings{Gogioso2017,
title = "Infinite-dimensional Categorical Quantum Mechanics",
author = "Gogioso, Stefano and Genovese, Fabrizio",
year = "2017",
series = "EPTCS",
booktitle = "QPL 2016",
pages = "51--69",
volume = "236",
note = "\doi{10.4204/EPTCS.236.4} \arXiv{1605.04305v2}"
}
@phdthesis{malherbe2013categorical,
title={Categorical models of computation: partially traced categories and presheaf models of quantum computation},
author={Malherbe, Octavio},
note={\arXiv{1301.5087v1}},
year={2010},
school={University of Ottawa}
}
@article{hasuo2017semantics,
title={Semantics of higher-order quantum computation via geometry of interaction},
author={Hasuo, Ichiro and Hoshino, Naohiko},
journal={Annals of Pure and Applied Logic},
volume={168},
number={2},
pages={404--469},
year={2017},
note={\doi{10.1016/j.apal.2016.10.010}}
}
@inproceedings{pagani2014applying,
title={Applying quantitative semantics to higher-order quantum computing},
author={Pagani, Michele and Selinger, Peter and Valiron, Beno{\^\i}t},
booktitle={POPL 2014},
series={ACM SIGPLAN Notices},
volume={49},
number={1},
pages={647--658},
year={2014},
note={\doi{10.1145/2535838.2535879} \arXiv{1311.2290v1}}
}
@inproceedings{furber2013kleisli,
title={From {K}leisli categories to commutative {$C^*$}-algebras: probabilistic {G}elfand duality},
author={Furber, Robert W.J. and Jacobs, Bart P.F.},
series={LNCS},
volume={8089},
booktitle={CALCO 2013},
pages={141--157},
year={2013},
note={\doi{10.1007/978-3-642-40206-7\_12}}
}
@misc{riesz,
author = {van Rooij, Arnoud C.M.},
title = {Riesz spaces},
year = {2011},
institution = {Radboud University},
howpublished = {\url{https://github.com/awesterb/riesz-spaces}}
}
@book{conway2000,
title={A course in operator theory},
author={Conway, John B.},
year={2000},
note={\doi{10.1090/gsm/021}}
}
@book{conway2013,
title={A course in functional analysis},
author={Conway, John B.},
year={1985},
note={\doi{10.1007/978-1-4757-3828-5}}
}
@book{kr,
title={Fundamentals of the Theory of Operator Algebras, I \& II},
author={Kadison, Richard V. and Ringrose, John R.},
year={1983},
note={\doi{10.1090/gsm/015} \& \doi{10.1090/gsm/016}}
}
@article{stinespring,
title={Positive functions on {C}*-algebras},
author={Stinespring, W. Forrest},
journal={Proceedings of the American Mathematical Society},
volume={6},
number={2},
pages={211--216},
year={1955},
publisher={JSTOR},
note={\doi{10.2307/2032342}}
}
@article{paschke,
title={Inner product modules over {B}*-algebras},
author={Paschke, William L.},
journal={Transactions of the American Mathematical Society},
volume={182},
pages={443--468},
year={1973},
note={\doi{10.1090/S0002-9947-1973-0355613-0}}
}
@article{sokal,
author = {Sokal, Alan D.},
journal = {The American Mathematical Monthly},
number = {5},
pages = {450-452},
publisher = {Mathematical Association of America},
title = {A Really Simple Elementary Proof of the Uniform Boundedness Theorem},
volume = {118},
year = {2011},
note = {\doi{10.4169/amer.math.monthly.118.05.450}}
}
@article{lindblad,
title={Completely positive maps and entropy inequalities},
author={Lindblad, G{\"o}ran},
journal={Communications in Mathematical Physics},
volume={40},
number={2},
pages={147--151},
year={1975},
publisher={Springer}
}
@article{werner,
title={Optimal cloning of pure states},
author={Werner, Reinhard F.},
journal={Physical Review A},
volume={58},
number={3},
pages={1827},
year={1998},
publisher={APS},
note={\doi{10.1103/PhysRevA.58.1827}}
}
@inproceedings{staton,
title={Algebraic effects, linearity, and quantum programming languages},
author={Staton, Sam},
booktitle={ACM SIGPLAN Notices},
volume={50},
pages={395--406},
year={2015},
organization={ACM},
note={\doi{10.1145/2676726.2676999}}
}
@article{werner2,
title={The information-disturbance tradeoff and the continuity of {Stinespring}'s representation},
author={Kretschmann, Dennis and Schlingemann, Dirk and Werner, Reinhard F.},
journal={Information Theory, IEEE Transactions on},
volume={54},
number={4},
pages={1708--1717},
year={2008},
publisher={IEEE},
note={\doi{10.1109/TIT.2008.917696}}
}
@Inproceedings{prakash,
author = {B\u{a}descu, Costin and Panangaden, Prakash},
year = {2015},
title = {Quantum Alternation: Prospects and Problems},
booktitle = {QPL 2015},
series = {EPTCS},
volume = {195},
publisher = {Open Publishing Association},
pages = {33-42},
note = {\doi{10.4204/EPTCS.195.3}},
}
@article{selinger,
title={Dagger compact closed categories and completely positive maps},
author={Selinger, Peter},
journal={ENTCS},
volume={170},
pages={139--163},
year={2007},
publisher={Elsevier},
note={\doi{10.1016/j.entcs.2006.12.018}}
}
@article{chiribella,
title={Informational derivation of quantum theory},
author={Chiribella, Giulio and D'Ariano, Giacomo Mauro and Perinotti, Paolo},
journal={Physical Review A},
volume={84},
number={1},
pages={012311},
year={2011},
publisher={APS},
note={\doi{10.1103/PhysRevA.84.012311}}
}
@inproceedings{wwpaschke,
author = {Westerbaan, Abraham A. and Westerbaan, Bas E.},
year = {2017},
title = {Paschke Dilations},
booktitle = {QPL 2016},
journal = {EPTCS},
volume = {236},
pages = {229--244},
note = {\doi{10.4204/EPTCS.236.15} \arXiv{1603.04353v2}}
}
@book{paulsen,
AUTHOR = {Paulsen, Vern I.},
TITLE = {Completely bounded maps and operator algebras},
SERIES = {Cambridge Studies in Advanced Mathematics},
VOLUME = {78},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {2002},
}
@article{russodye,
author = "Russo, Bernard and Dye, H. A.",
note = "\doi{10.1215/S0012-7094-66-03346-1}",
journal = "Duke Mathematical Journal",
number = "2",
pages = "413--416",
title = "A note on unitary operators in {{$C^*$}}-algebras",
volume = "33",
year = "1966",
note = "\doi{10.1215/S0012-7094-66-03346-1}"
}
@article{choi,
title={A {Schwarz} Inequality for Positive Linear Maps on {C}*-algebras},
author={Choi, Man--Duen},
journal={Illinois Journal of Mathematics},
volume={18},
number={4},
pages={565--574},
year={1974},
note={\doi{10.1215/ijm/1256051007}}
}
@book{willard,
title={General topology},
author={Willard, Stephen},
year={1970},
publisher={Addison--Wesley}
}
@MISC {ref1382,
TITLE = {Reference request unital normal *-homomorphisms {$B(H) \to B(K)$}},
AUTHOR = {Westerbaan, Abraham A.~and Westerbaan, Bas E.},
HOWPUBLISHED = {Mathematics Stack Exchange},
NOTE = {\url{https://math.stackexchange.com/q/3140021} (version: 2019-03-11)},
}
@MISC {stineinj,
TITLE = {When does {Stinespring} dilation yield a faithful representation?},
author={Westerbaan, Abraham A. and Westerbaan, Bas E.},
HOWPUBLISHED = {Mathematics Stack Exchange},
NOTE = {\url{http://math.stackexchange.com/q/1701574} (version: 2016-03-17)},
}
@book{lance,
title={Hilbert {C}*-modules: a toolkit for operator algebraists},
author={Lance, E. Christopher},
volume={210},
year={1995},
publisher={Cambridge University Press},
note={\doi{10.1017/CBO9780511526206}}
}
@article{pedersen1972,
title={Some operator monotone functions},
author={Pedersen, Gert K.},
journal={Proceedings of the American Mathematical Society},
volume={36},
number={1},
pages={309--310},
year={1972},
note={\doi{10.1090/S0002-9939-1972-0306957-4}}
}
@article{pedersen1979c,
title={C*-algebras and their automorphism groups},
author={Pedersen, Gert K.},
journal={London Mathematical Society Monographs},
year={1979},
publisher={Academic press}
}
@article{douglas,
title={{On majorization, factorization, and range inclusion of operators on {H}ilbert space}},
author={Douglas, Ronald G.},
journal={Proceedings of the American Mathematical Society},
volume={17},
number={2},
pages={413--415},
year={1966},
note={\doi{10.1090/S0002-9939-1966-0203464-1}}
}
@article{arveson,
title={Subalgebras of {C}*-algebras},
author={Arveson, William B.},
journal={Acta Mathematica},
volume={123},
number={1},
pages={141--224},
year={1969},
publisher={Springer},
note={\doi{10.1007/BF02392388}}
}
@article{jacobs2009orthomodular,
TITLE = {Orthomodular lattices, {Foulis} Semigroups and Dagger Kernel Categories},
AUTHOR = {Jacobs, Bart P.F.},
note = {\doi{10.2168/LMCS-6(2:1)2010} \arXiv{0912.0931}},
JOURNAL = {LMCS},
VOLUME = {6},
issue = {2},
YEAR = {2010},
MONTH = Jun,
}
@Inproceedings{kentapartial,
author = {Cho, Kenta},
year = {2015},
title = {Total and Partial Computation in Categorical Quantum Foundations},
booktitle = {QPL 2015},
series = {EPTCS},
volume = {195},
pages = {116-135},
note = {\doi{10.4204/EPTCS.195.9} \arXiv{1511.01569v1}},
}
@unpublished{effintro,
title={An introduction to effectus theory},
author={Cho, Kenta and Jacobs, Bart P.F. and Westerbaan, Bas E. and Westerbaan, Abraham A.},
note={\arXiv{1512.05813v1}},
year={2015}
}
@article{newdirections,
year = {2015},
volume = {11},
number = {3},
author = {Jacobs, Bart P.F.},
title = {New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic},
journal = {LMCS},
note = {\doi{10.2168/LMCS-11(3:24)2015} \arXiv{1205.3940v5}}
}
@inproceedings{statesofconvexsets,
author="Jacobs, Bart P.F.
and Westerbaan, Bas E.
and Westerbaan, Abraham A.",
title="States of Convex Sets",
booktitle="FoSSaCS 2015",
series="LNCS",
volume="9034",
year="2015",
pages="87--101",
note="\doi{10.1007/978-3-662-46678-0\_6}",
}
@article{arbib,
title={Partially additive categories and flow-diagram semantics},
author={Arbib, Michael A. and Manes, Ernest G.},
journal={Journal of Algebra},
volume={62},
number={1},
pages={203--227},
year={1980},
publisher={Elsevier},
note="\doi{10.1016/0021-8693(80)90212-4}"
}
@article{ea,
title={Effect algebras and unsharp quantum logics},
author={Foulis, David J. and Bennett, Mary K.},
journal={Foundations of Physics},
volume={24},
number={10},
pages={1331--1352},
year={1994},
publisher={Springer},
note={\doi{10.1007/BF02283036}}
}
@article{basmsc,
title={Sequential product on effect logics},
author={Westerbaan, Bas E.},
note={Master's thesis, Radboud University.
\url{https://www.ru.nl/publish/pages/813276/masterscriptie_bas_westerbaan.pdf}},
year={2013}
}
@article{corefl,
title={Coreflections in algebraic quantum logic},
author={Jacobs, Bart P.F. and Mandemaker, Jorik},
journal={Foundations of physics},
volume={42},
number={7},
pages={932--958},
year={2012},
publisher={Springer},
note={\doi{10.1007/s10701-012-9654-8}}
}
@article{probdistrconv,
title={Probabilities, distribution monads, and convex categories},
author={Jacobs, Bart P.F.},
journal={Theoretical Computer Science},
volume={412},
number={28},
pages={3323--3336},
year={2011},
publisher={Elsevier},
note={\doi{10.1016/j.tcs.2011.04.005}}
}
@article{gudder1998representation,
title={Representation theorem for convex effect algebras},
author={Gudder, Stanley P. and Pulmannov{\'a}, Sylvia},
journal={Commentationes Mathematicae Universitatis Carolinae},
volume={39},
number={4},
pages={645--660},
year={1998},
publisher={Prague [Mathematical Institute of the Charles University]}
}
@article{gudder1999convex,
title={Convex structures and effect algebras},
author={Gudder, Stanley P.},
journal={International Journal of Theoretical Physics},
volume={38},
number={12},
pages={3179--3187},
year={1999},
publisher={Springer},
note={\doi{10.1023/A:1026678114856}}
}
@article{jacobs2016expectation,
title={The expectation monad in quantum foundations},
author={Jacobs, Bart P.F. and Mandemaker, Jorik and Furber, Robert W.J.},
journal={Information and Computation},
volume={250},
pages={87--114},
year={2016},
note={\doi{10.1016/j.ic.2016.02.009}}
}
@article{neumann1970quasivariety,
title={On the quasivariety of convex subsets of affine spaces},
author={Neumann, Walter D.},
journal={Archiv der Mathematik},
volume={21},
number={1},
pages={11--16},
year={1970},
publisher={Springer},
note={\doi{10.1007/BF01220869}}
}
@article{flood1981semiconvex,
title={Semiconvex geometry},
author={Flood, Joe},
journal={Journal of the Australian Mathematical Society},
volume={30},
number={4},
pages={496--510},
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