Luigi Accardi & Carlo Cecchini (1982):
Conditional expectations in von Neumann algebras and a theorem of Takesaki.
J. Funct. Anal. 45(2),
pp. 245–273,
doi:10.1016/0022-1236(82)90022-2.
Howard Barnum, Jonathan Barrett, Matthew Leifer & Alexander Wilce (2007):
Generalized No-Broadcasting Theorem.
Phys. Rev. Lett. 99,
pp. 240501,
doi:10.1103/PhysRevLett.99.240501.
Howard Barnum & Emanuel Knill (2002):
Reversing quantum dynamics with near-optimal quantum and classical fidelity.
J. Math. Phys. 43(5),
pp. 2097–2106,
doi:10.1063/1.1459754.
David Bohm (1951):
Quantum theory.
Prentice-Hall,
Englewood Cliffs, NJ.
Also as reprint ed.: New York, NY, Dover Publications, 1989.
Kenta Cho & Bart Jacobs (2019):
Disintegration and Bayesian inversion via string diagrams.
Math. Struct. Comp. Sci.,
pp. 1–34,
doi:10.1017/S0960129518000488.
Florence Clerc, Vincent Danos, Fredrik Dahlqvist & Ilias Garnier (2017):
Pointless learning.
In: Foundations of software science and computation structures,
Lecture Notes in Comput. Sci. 10203.
Springer, Berlin,
pp. 355–369,
doi:10.1007/978-3-662-54458-7_21.
Bob Coecke & Robert W. Spekkens (2012):
Picturing classical and quantum Bayesian inference.
Synthese 186(3),
pp. 651–696,
doi:10.1007/s11229-011-9917-5.
Jared Culbertson & Kirk Sturtz (2014):
A categorical foundation for Bayesian probability.
Appl. Categ. Structures 22(4),
pp. 647–662,
doi:10.1007/s10485-013-9324-9.
Fredrik Dahlqvist, Vincent Danos, Ilias Garnier & Ohad Kammar (2016):
Bayesian Inversion by Omega-Complete Cone Duality.
In: Josée Desharnais & Radha Jagadeesan: 27th International Conference on Concurrency Theory (CONCUR 2016),
Leibniz International Proceedings in Informatics (LIPIcs) 59.
Schloss Dagstuhl–Leibniz–Zentrum fuer Informatik,
pp. 1:1–1:15,
doi:10.4230/LIPIcs.CONCUR.2016.1.
Albert Einstein, Boris Podolsky & Nathan Rosen (1935):
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?.
Phys. Rev. 47,
pp. 777–780,
doi:10.1103/PhysRev.47.777.
Douglas R. Farenick (2001):
Algebras of linear transformations.
Universitext.
Springer-Verlag, New York,
doi:10.1007/978-1-4613-0097-7.
Brendan Fong (2012):
Causal theories: A categorical perspective on Bayesian networks.
University of Oxford.
University of Oxford. Available at arXiv:1301.6201 [math.PR].
Tobias Fritz (2020):
A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics.
Adv. Math. 370,
pp. 107239,
doi:10.1016/j.aim.2020.107239.
Robert Furber & Bart Jacobs (2015):
From Kleisli categories to commutative C^*-algebras: probabilistic Gelfand duality.
Log. Methods Comput. Sci. 11(2),
pp. 1:5, 28,
doi:10.2168/LMCS-11(2:5)2015.
Bart Jacobs (2019):
Lower and Upper Conditioning in Quantum Bayesian Theory.
In: Peter Selinger & Giulio Chiribella: Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, Canada, 3-7th June 2018,
Electronic Proceedings in Theoretical Computer Science 287.
Open Publishing Association,
pp. 225–238,
doi:10.4204/EPTCS.287.13.
Matthew S. Leifer (2006):
Quantum dynamics as an analog of conditional probability.
Phys. Rev. A 74,
pp. 042310,
doi:10.1103/PhysRevA.74.042310.
Matthew S. Leifer & Robert W. Spekkens (2013):
Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference.
Phys. Rev. A 88,
pp. 052130,
doi:10.1103/PhysRevA.88.052130.
Hans Maassen (2010):
Quantum probability and quantum information theory.
In: Quantum information, computation and cryptography,
Lect. Notes Physics.
Springer,
pp. 65–108,
doi:10.1007/978-3-642-11914-9_3.
Arthur J. Parzygnat (2017):
Discrete probabilistic and algebraic dynamics: a stochastic Gelfand–Naimark Theorem.
ArXiv preprint: 1708.00091 [math.FA].
Arthur J. Parzygnat (2020):
Inverses, disintegrations, and Bayesian inversion in quantum Markov categories.
ArXiv preprint: 2001.08375 [quant-ph].
Arthur J. Parzygnat & Benjamin P. Russo (2019):
Non-commutative disintegrations: existence and uniqueness in finite dimensions.
ArXiv preprint: 1907.09689 [quant-ph].
Arthur J. Parzygnat & Benjamin P. Russo (2020):
A non-commutative Bayes' theorem.
ArXiv preprint: 2005.03886 [quant-ph].
Dénes Petz (1984):
A dual in von Neumann algebras with weights.
Q. J. Math 35(4),
pp. 475–483,
doi:10.1093/qmath/35.4.475.
Dénes Petz (1988):
Sufficiency of channels over von Neumann algebras.
Q. J. Math. 39(1),
pp. 97–108,
doi:10.1093/qmath/39.1.97.
Peter Selinger (2010):
A Survey of Graphical Languages for Monoidal Categories.
Lect. Notes Phys.,
pp. 289–355,
doi:10.1007/978-3-642-12821-9_4.
Masamichi Takesaki (1970):
Tomita's theory of modular Hilbert algebras and its applications.
Lecture Notes in Mathematics 128.
Springer,
doi:10.1007/BFb0065832.
Armin Uhlmann (2016):
Anti- (Conjugate) Linearity.
Sci. China Phys. Mech. Astron. 59(3),
pp. 630301,
doi:10.1007/s11433-015-5777-1.