Chris Heunen

Categories for Quantum Theory

C. Heunen and J. Vicary

Oxford University Press, 2019

[book] [review] [errata]

Compact inverse categories

R. Cockett and C. Heunen

[pdf] [preprint]

Monoidal characterisation of groupoids and connectors

M. Gran, C. Heunen, and S. Tull

Topology and its Applications, 106966, 2019

[pdf] [preprint] [journal]

Ontological models for quantum theory as functors

A. Gheorghiu and C. Heunen

Quantum Physics and Logic 2019

[pdf] [preprint]

Topos quantum theory with short posets

J. Harding and C. Heunen

Order, 2020

[pdf] [preprint] [journal]

Automated distribution of quantum circuits

P. Andres Martinez and C. Heunen

Physical Review A 100:032308, 2019

[pdf] [preprint] [journal]

Tensor topology

P. Enrique Moliner, C. Heunen, and S. Tull

Journal of Pure and Applied Algebra 224(10):106378, 2020

[pdf] [preprint] [journal]

Limits in dagger categories

C. Heunen and M. Karvonen

Theory and Applications of Categories 34(18):468-513, 2019

[pdf] [preprint] [journal] [review] [review]

Boolean subalgebras of orthoalgebras

J. Harding, C. Heunen, Bert Lindenhovius, and M. Navara

Order 36(3):563--609, 2019

[pdf] [preprint] [journal] [review]

Reversible effects as inverse arrows

C. Heunen, R. Kaarsgaard and M. Karvonen

Mathematical Foundations of Programming Semantics, ENTCS 341:179-199, 2018

[pdf] [preprint] [proceedings]

Denotational validation of higher-order Bayesian inference

A. Scibior, O. Kammar, M. Vakar, S. Staton, H. Yang, Y. Cai, K. Ostermann, S. Moss, C. Heunen, Z. Ghahramani

Proceedings of the ACM on Principles of Programming Languages 2:60, 2018.

[pdf] [preprint] [proceedings]

Purity through factorisation

O. Cunningham and C. Heunen

(EPTCS 266:315-328) proceedings of Quantum Physics and Logic, 2017.

[pdf] [preprint] [proceedings]

Space in monoidal categories

P. Enrique Moliner, C. Heunen, and S. Tull

(EPTCS 266:399-410) proceedings of Quantum Physics and Logic, 2017.

[pdf] [preprint] [proceedings]

Frobenius structures over Hilbert C*-modules

C. Heunen and M. L. Reyes

Communications in Mathematical Physics 361(2):787--824, 2018

[pdf] [preprint] [journal] [review] [review] [video]

A convenient category for higher-order probability theory

C. Heunen, O. Kammar, S. Staton, and H. Yang

Logic in Computer Science, 2017.

[pdf] [preprint] [proceedings]

Proceedings of the 13th International Conference on Quantum Physics and Logic

R. Duncan and C. Heunen (editors)

Electronic Proceedings in Theoretical Computer Science 236, 2017.

[proceedings]

Can a quantum state over time resemble a quantum state at a single time?

D. Horsman and C. Heunen and M. F. Pusey and J. Barrett and R. W. Spekkens

Proceedings of the Royal Society A 473(2205):20170395, 2017.

[pdf] [preprint] [journal]

Discretization of C*-algebras

C. Heunen and M. L. Reyes

Journal of Operator Theory 77(1):19-37, 2017

[pdf] [preprint] [journal] [review]

Pictures of complete positivity in arbitrary dimension

B. Coecke and C. Heunen

Information and Computation 250:50-58, 2016

[pdf] [preprint] [journal] [review]

(EPTCS 95:27-35) in the proceedings of Quantum Physics and Logic VIII, 2011

[pdf] [preprint] [proceedings]

Can quantum theory be characterized in terms of information-theoretic constraints?

C. Heunen and A. Kissinger

[pdf] [preprint]

Monads on dagger categories

C. Heunen and M. Karvonen

Theory and Applications of Categories 31(35):1016-1043, 2016

[pdf] [preprint] [journal] [review] [review]

Reversible monadic programming

(ENTCS 319:217--237) proceedings of Mathematical Foundations of Programming Semantics, 2015

[pdf] [preprint] [proceedings] [review]

Semantics for probablistic programming: higher-order functions, continuous distributions, soft constraints

S. Staton, H. Yang, C. Heunen, O. Kammar, and F. Wood

Logic in Computer Science 525--534, 2016

[pdf] [preprint] [proceedings]

The category of matroids

C. Heunen and V. Patta

Applied Categorical Structures 26(2):205-237, 2017.

[pdf] [preprint] [journal] [review] [review]

Proceedings of the 12th International Workshop on Quantum Physics and Logic

C. Heunen, P. Selinger, and J. Vicary (editors)

Electronic Proceedings in Theoretical Computer Science 195, 2015

[proceedings]

Categories of relations as models of quantum theory

C. Heunen and S. Tull

(EPTCS 195:247-261) In the proceedings of Quantum Physics and Logic , 2015

[pdf] [preprint] [proceedings] [review]

Axiomatizing complete positivity

O. Cunningham and C. Heunen

(EPTCS 195:148--157) In the proceedings of Quantum Physics and Logic , 2015

[pdf] [preprint] [proceedings] [review]

Domains of commutative C*-subalgebras

C. Heunen and B. Lindenhovius

Proceedings of the 30th annual ACM/IEEE symposium on Logic in Computer Science 450-461, 2015

[pdf] [preprint] [proceedings]

Mathematical Structures in Computer Science, 29(7):972--1006, 2019

[pdf] [preprint] [journal]

The many classical faces of quantum structures

C. Heunen

Entropy 19(4):144, 2017.

[pdf] [preprint] [journal]

Book review: Foundations of relational realism

M. Epperson and E. Zafiris

Studies in History and Philosophy of Modern Physics 99-100, 2014

[journal]

Mixed quantum states in higher categories

C. Heunen, J. Vicary, and L. Wester

(EPTCS 172:304-315) In the proceedings of Quantum Physics and Logic XI, 2014

[pdf] [preprint] [proceedings]

Categories of quantum and classical channels

B. Coecke, C. Heunen, and A. Kissinger

Quantum Information Processing 15(12):5179--5209, 2016

[pdf] [preprint] [journal]

(EPTCS 158:1-14) in the proceedings of Quantum Physics and Logic IX, 2012

[pdf] [preprint] [proceedings]

Extending obstructions to noncommutative functorial spectra

B. van den Berg and C. Heunen

Theory and Applications of Categories 29(17):457--474, 2014

[pdf] [preprint] [journal] [review] [review]

No-go theorems for functorial localic spectra of noncommutative rings

(EPTCS 95:21-25) in the proceedings of Quantum Physics and Logic VIII, 2011

[pdf] [preprint] [proceedings]

Operational theories and categorical quantum mechanics

S. Abramsky and C. Heunen

Logic and algebraic structures in quantum computing and information,
Cambridge University Press, Lecture Notes in Logic 45:88-122, 2016

[pdf] [preprint] [book]

Piecewise Boolean algebras and their domains

C. Heunen

Proceedings of the 41st International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 8573: 208-219, 2014

[pdf] [preprint] [proceedings]

Characterizations of categories of commutative C*-subalgebras

C. Heunen

Communications in Mathematical Physics 331(1):215-238, 2014

[pdf] [preprint] [journal] [review]

Quantum realization of arbitrary joint measurability structures

R. Kunjwal, C. Heunen, and T. Fritz

Physical Review A 89(5):052126, 2014

[pdf] [preprint] [journal]

Active lattices determine AW*-algebras

C. Heunen and M. L. Reyes

Journal of Mathematical Analysis and Applications 416:289-313, 2014

[pdf] [preprint] [journal] [review]

Quantum theory realises all joint measurability graphs

C. Heunen, T. Fritz, and M. L. Reyes

Physical Review A 89(3):032121, 2014

[pdf] [preprint] [journal]

Matrix multiplication is determined by orthogonality and trace

C. Heunen and C. Horsman

Linear Algebra and its Applications 439(12):4130-4134, 2013

[pdf] [preprint] [journal] [review]

Completely positive projections and biproducts

C. Heunen, A. Kissinger, and P. Selinger

(EPTCS 171:71--83) In the proceedings of Quantum Physics and Logic X, 2014

[pdf] [preprint] [proceedings]

On the functor l²

C. Heunen

Computation, Logic, Games, and Quantum Foundations: 107-121, 2013

[pdf] [preprint] [book] [erratum]

Compositional quantum logic

B. Coecke, C. Heunen, and A. Kissinger

Computation, Logic, Games, and Quantum Foundations: 21-36, 2013

[pdf] [preprint] [book] [review]

Diagonalizing matrices over AW*-algebras

C. Heunen and M. L. Reyes

Journal of Functional Analysis 264(8):1873-1898, 2013

[pdf] [preprint] [journal] [review] [review]

Relative Frobenius algebras are groupoids

C. Heunen, I. Contreras, and A. S. Cattaneo

Journal of Pure and Applied Algebra 217:114-124, 2013

[pdf] [preprint] [journal] [review]

Quantum physics and linguistics: a compositional, diagrammatic discourse

C. Heunen, M. Sadrzadeh, and E. Grefenstette (editors)

Oxford University Press, 2013

[book]

Completely positive classical structures and sequentializable quantum protocols

C. Heunen and S. Boixo

(EPTCS 95:91-101) in the proceedings of Quantum Physics and Logic VIII, 2011

[pdf] [preprint] [proceedings]

H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics

S. Abramsky and C. Heunen

Clifford Lectures, AMS Proceedings of Symposia in Applied Mathematics 71:1--24, 2012

[pdf] [preprint] [book] [review] [review]

Entangled and sequential quantum protocols with dephasing

S. Boixo and C. Heunen

Physical Review Letters 108:120402, 2012

[pdf] [preprint] [journal]

Complementarity in categorical quantum mechanics

C. Heunen

Foundations of Physics 42(7): 856--873, 2012

[pdf] [preprint] [journal] [review]

Noncommutativity as a colimit

B. van den Berg and C. Heunen

Applied Categorical Structures 20(4):393--414, 2012

[pdf] [preprint] [journal] [erratum] [review] [review]

Bohrification of operator algebras and quantum logic

C. Heunen, N.P. Landsman, and B. Spitters

Synthese 186(3):719--752, 2012

[pdf] [preprint] [journal]

The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach

C. Heunen, N.P. Landsman, B. Spitters, and S. Wolters

Journal of the Australian Mathematical Society 90:39--52, 2011

[pdf] [preprint] [journal] [review] [review]

Bohrification

C. Heunen, N.P. Landsman, and B. Spitters

chapter in "Deep Beauty" (editor: H. Halvorson), 2011

[pdf] [preprint] [book] [review] [review]

Quantum logic in dagger kernel categories

C. Heunen and B. Jacobs

Order 27(2):177-212, 2010

[pdf] [preprint] [journal] [review]

(ENTCS 270(2):79-103) in the proceedings of Quantum Physics and Logic VI, 2009

[pdf] [preprint] [proceedings]

Coalgebraic components in a many-sorted microcosm

I. Hasuo, C. Heunen, B. Jacobs, and A Sokolova

(LNCS 5728:64-80) in the proceedings of CALCO, 2009

[pdf] [proceedings]

Intuitionistic quantum logic of an n-level system

M. Caspers, C. Heunen, N.P. Landsman, and B. Spitters

Foundations of Physics, 39(7):731-759, 2009

[pdf] [preprint] [journal] [review] [review]

A topos for algebraic quantum theory

C. Heunen, N.P. Landsman, and B. Spitters

Communications in Mathematical Physics, 291:63--110, 2009

[pdf] [preprint] [journal]

Categorical quantum models and logics

C. Heunen

Amsterdam University Press, 2009
Ph.D. thesis, supervised by B. Jacobs and N.P. Landsman

Japanese edition published by Kyoritsu Shuppan, 2018

[pdf] [publisher] [hardcopies available on request] [Japanese publisher] [presentation: slides, text]

Categorical semantics for Arrows

B. Jacobs, C. Heunen, and I. Hasuo

Journal of Functional Programming, 19(3-4):403-438, 2009

[pdf] [journal] [review]

An embedding theorem for Hilbert categories

C. Heunen

Theory and Applications of Categories 22(13):321-344, 2009

[pdf] [preprint] [journal]

Semimodule enrichment

C. Heunen

(ENTCS 218:193-208) in the proceedings of MFPS XXIV, 2008

[pdf] [proceedings]

Compactly accessible categories and quantum key distribution

C. Heunen

Logical Methods in Computer Science, 4(4), 2008

[pdf] [journal]

The principle of general tovariance

C. Heunen, N.P. Landsman, and B. Spitters

(AIP Conf Proc 1023:93-102) in the proceedings of International Fall Workshop on Geometry and Physics XVI, 2008

[pdf] [discussion] [preprint] [proceedings]

Arrows, like Monads, are Monoids

C. Heunen and B. Jacobs

(ENTCS 158:219-236) in the proceedings of MFPS 22, 2006

[pdf] [proceedings]

Tensegrities, of houtje-touwtje-figuren

C. Heunen and D. van Leijenhorst

Nieuw Archief voor Wiskunde 2004(4):279--283, 2004

[pdf] [journal]

Accurate silhouettes -- do polyhedral models suffice?

C. Heunen

GMAG'03 proceedings, 69-74, IEEE, 2003

[pdf] [proceedings]

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