@article(AcCe82,
author = {Luigi Accardi and Carlo Cecchini},
year = {1982},
title = {Conditional expectations in von {N}eumann algebras and a theorem of {T}akesaki},
journal = {J. Funct. Anal.},
volume = {45},
number = {2},
pages = {245--273},
doi = {10.1016/0022-1236(82)90022-2},
)
@article(BBLW,
author = {Howard Barnum and Jonathan Barrett and Matthew Leifer and Alexander Wilce},
year = {2007},
title = {Generalized No-Broadcasting Theorem},
journal = {Phys. Rev. Lett.},
volume = {99},
pages = {240501},
doi = {10.1103/PhysRevLett.99.240501},
)
@article(BaKn02,
author = {Howard Barnum and Emanuel Knill},
year = {2002},
title = {Reversing quantum dynamics with near-optimal quantum and classical fidelity},
journal = {J. Math. Phys.},
volume = {43},
number = {5},
pages = {2097--2106},
doi = {10.1063/1.1459754},
)
@book(Bo51,
author = {David Bohm},
year = {1951},
title = {{Quantum theory}},
publisher = {Prentice-Hall},
address = {Englewood Cliffs, {NJ}},
note = {Also as reprint ed.: New York, NY, Dover Publications, 1989},
)
@article(ChJa18,
author = {Kenta Cho and Bart Jacobs},
year = {2019},
title = {Disintegration and {B}ayesian inversion via string diagrams},
journal = {Math. Struct. Comp. Sci.},
pages = {1--34},
doi = {10.1017/S0960129518000488},
)
@incollection(CDDG17,
author = {Florence Clerc and Vincent Danos and Fredrik Dahlqvist and Ilias Garnier},
year = {2017},
title = {Pointless learning},
booktitle = {Foundations of software science and computation structures},
series = {Lecture Notes in Comput. Sci.},
volume = {10203},
publisher = {Springer, Berlin},
pages = {355--369},
doi = {10.1007/978-3-662-54458-7\_21},
)
@article(CoSp12,
author = {Bob Coecke and Robert W. Spekkens},
year = {2012},
title = {Picturing classical and quantum {B}ayesian inference},
journal = {Synthese},
volume = {186},
number = {3},
pages = {651--696},
doi = {10.1007/s11229-011-9917-5},
)
@article(CuSt14,
author = {Jared Culbertson and Kirk Sturtz},
year = {2014},
title = {A categorical foundation for {B}ayesian probability},
journal = {Appl. Categ. Structures},
volume = {22},
number = {4},
pages = {647--662},
doi = {10.1007/s10485-013-9324-9},
)
@incollection(DDGK16,
author = {Fredrik Dahlqvist and Vincent Danos and Ilias Garnier and Ohad Kammar},
year = {2016},
title = {Bayesian Inversion by Omega-Complete Cone Duality},
editor = {Jos\'ee Desharnais and Radha Jagadeesan},
booktitle = {27th International Conference on Concurrency Theory ({CONCUR} 2016)},
series = {Leibniz International Proceedings in Informatics ({LIPI}cs)},
volume = {59},
publisher = {Schloss Dagstuhl--Leibniz--Zentrum fuer Informatik},
pages = {1:1--1:15},
doi = {10.4230/LIPIcs.CONCUR.2016.1},
)
@article(EPR,
author = {Albert Einstein and Boris Podolsky and Nathan Rosen},
year = {1935},
title = {Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?},
journal = {Phys. Rev.},
volume = {47},
pages = {777--780},
doi = {10.1103/PhysRev.47.777},
)
@book(Fa01,
author = {Douglas R. Farenick},
year = {2001},
title = {Algebras of linear transformations},
series = {Universitext},
publisher = {Springer-Verlag, New York},
doi = {10.1007/978-1-4613-0097-7},
)
@mastersthesis(Fo12,
author = {Brendan Fong},
year = {2012},
title = {Causal theories: A categorical perspective on {B}ayesian networks},
school = {University of Oxford},
note = {University of Oxford. Available at arXiv:\href{https://arxiv.org/abs/1301.6201}{1301.6201 [math.PR]}},
)
@article(Fr19,
author = {Tobias Fritz},
year = {2020},
title = {A synthetic approach to {M}arkov kernels, conditional independence and theorems on sufficient statistics},
journal = {Adv. Math.},
volume = {370},
pages = {107239},
doi = {10.1016/j.aim.2020.107239},
)
@article(FuJa15,
author = {Robert Furber and Bart Jacobs},
year = {2015},
title = {From {K}leisli categories to commutative {$C^*$}-algebras: probabilistic {G}elfand duality},
journal = {Log. Methods Comput. Sci.},
volume = {11},
number = {2},
pages = {1:5, 28},
doi = {10.2168/LMCS-11(2:5)2015},
)
@inproceedings(Ja18EPTCS,
author = {Bart Jacobs},
year = {2019},
title = {Lower and Upper Conditioning in Quantum {B}ayesian Theory},
editor = {Peter Selinger and Giulio Chiribella},
booktitle = {{Proceedings of the 15th International Conference on} Quantum Physics and Logic, {{H}alifax, {C}anada, 3-7th June 2018}},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {287},
publisher = {Open Publishing Association},
pages = {225--238},
doi = {10.4204/EPTCS.287.13},
)
@article(Le06,
author = {Matthew S. Leifer},
year = {2006},
title = {Quantum dynamics as an analog of conditional probability},
journal = {Phys. Rev. A},
volume = {74},
pages = {042310},
doi = {10.1103/PhysRevA.74.042310},
)
@article(LeSp13,
author = {Matthew S. Leifer and Robert W. Spekkens},
year = {2013},
title = {Towards a formulation of quantum theory as a causally neutral theory of {B}ayesian inference},
journal = {Phys. Rev. A},
volume = {88},
pages = {052130},
doi = {10.1103/PhysRevA.88.052130},
)
@incollection(Ma10,
author = {Hans Maassen},
year = {2010},
title = {Quantum probability and quantum information theory},
booktitle = {Quantum information, computation and cryptography},
series = {Lect. Notes Physics},
publisher = {Springer},
pages = {65--108},
doi = {10.1007/978-3-642-11914-9\_3},
)
@misc(Pa17,
author = {Arthur J. Parzygnat},
year = {2017},
title = {Discrete probabilistic and algebraic dynamics: a stochastic {G}elfand--{N}aimark Theorem},
note = {ArXiv preprint: \href{https://arxiv.org/abs/1708.00091}{1708.00091 [math.FA]}},
)
@misc(PaBayes,
author = {Arthur J. Parzygnat},
year = {2020},
title = {Inverses, disintegrations, and {B}ayesian inversion in quantum {M}arkov categories},
note = {ArXiv preprint: \href{https://arxiv.org/abs/2001.08375}{2001.08375 [quant-ph]}},
)
@misc(PaRu19,
author = {Arthur J. Parzygnat and Benjamin P. Russo},
year = {2019},
title = {Non-commutative disintegrations: existence and uniqueness in finite dimensions},
note = {ArXiv preprint: \href{https://arxiv.org/abs/1907.09689}{1907.09689 [quant-ph]}},
)
@misc(PaRuBayes,
author = {Arthur J. Parzygnat and Benjamin P. Russo},
year = {2020},
title = {A non-commutative {B}ayes' theorem},
note = {ArXiv preprint: \href{https://arxiv.org/abs/2005.03886}{2005.03886 [quant-ph]}},
)
@article(Pe84,
author = {D{\'e}nes Petz},
year = {1984},
title = {A dual in von~{N}eumann algebras with weights},
journal = {Q. J. Math},
volume = {35},
number = {4},
pages = {475--483},
doi = {10.1093/qmath/35.4.475},
)
@article(Pe88,
author = {D{\'e}nes Petz},
year = {1988},
title = {Sufficiency of channels over von~{N}eumann algebras},
journal = {Q. J. Math.},
volume = {39},
number = {1},
pages = {97--108},
doi = {10.1093/qmath/39.1.97},
)
@article(Se10,
author = {Peter Selinger},
year = {2010},
title = {A Survey of Graphical Languages for Monoidal Categories},
journal = {Lect. Notes Phys.},
pages = {289--355},
doi = {10.1007/978-3-642-12821-9\_4},
)
@book(Tak70book,
author = {Masamichi Takesaki},
year = {1970},
title = {{T}omita's theory of modular {H}ilbert algebras and its applications},
series = {Lecture Notes in Mathematics},
volume = {128},
publisher = {Springer},
doi = {10.1007/BFb0065832},
)
@article(Uh16,
author = {Armin Uhlmann},
year = {2016},
title = {Anti- (Conjugate) Linearity},
journal = {Sci. China Phys. Mech. Astron.},
volume = {59},
number = {3},
pages = {630301},
doi = {10.1007/s11433-015-5777-1},
)