Chris Heunen

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Categories for Quantum Theory
C. Heunen and J. Vicary
Oxford University Press, 2019
[book] [ebook] [review] [review] [errata]
Japanese edition, translated by H. Kawabe
Morikita publishing, 2021
[book] [book] [review]
Qurts: Automatic quantum uncomputation by affine types with lilfetime
K. Hirata, C. Heunen
Principles of Programming Languages (POPL) 2025
[preprint]
A brief review of quantum machine learning for financial services
M. Doosti, P. Wallden, C. B. Hamill, R. Hankache, O. T. Brown, C. Heunen
[preprint]
Compositional reversible computation
J. Carette, C. Heunen, R. Kaarsgaard, and A. Sabry
Reversible Computation, LNCS 14680:10-27, 2024.
[preprint] [proceedings]
Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
M. Di Meglio and C. Heunen
[preprint] [post]
With a few square roots, quantum computing is as easy as Pi
J. Carette, C. Heunen, R. Kaarsgaard, and A. Sabry
ACM Principles of Programming Languages 8:546--574, 2024
[preprint] [proceedings] [press]
Categories of sets with infinite addition
P. Andres-Martinez and C. Heunen
[preprint]
Ordered locales
C. Heunen and N. van der Schaaf
Journal of Pure and Applied Algebra 107654, 2024.
[preprint] [journal]
The quantum effect: a recipe for Quantum Pi
J. Carette, C. Heunen, R. Kaarsgaard, and A. Sabry
Proceedings of the ACM on Programming Languages 8(236):1--29, 2024
[preprint] [journal] [code]
Axioms for the category of Hilbert spaces and linear contractions
C. Heunen, A. Kornell, and N. van der Schaaf
Bulletin of the London Mathematical Society 56(4):1532-1549, 2024.
[preprint] [journal] [review]
Duoidally enriched Freyd categories
C. Heunen and J. Sigal
Proceedings of Relational and Algebraic Methods in Computer Science (RAMiCS) LNCS 13896:241-257, 2023
[preprint] [proceedings]
Universal properties of partial quantum maps
P. Andres-Martinez, C. Heunen, and R. Kaarsgaard
Quantum Physics and Logic, Electronic Proceedings in Theoretical Computer Science 394:192-207, 2023.
[preprint] [proceedings]
Axioms for the category of Hilbert spaces
C. Heunen and A. Kornell
Proceedings of the National Academy of Sciences 119(9):e2117024119, 2022.
[preprint] [journal] [review] [post] [press] [video] [slides]
Proceedings of the 18th International Conference on Quantum Physics and Logic
M. Backens and C. Heunen (editors)
Electronic Proceedings in Theoretical Computer Science 343, 2021.
[proceedings]
Localisable Monads
C. Constantin, N. Dicaire, and C. Heunen
Computer Science Logic LIPICS 15:1--17, 2022.
[preprint] [proceedings]
Quantum Information Effects
C. Heunen and R. Kaarsgaard
Proceedings of the ACM on Programming Languages (POPL) 6:1-27, 2022.
[preprint] [proceedings] [code] [press]
Sheaf representation of monoidal categories
R. Soares Barbosa and C. Heunen
Advances in Mathematics 416:108900, 2023.
[preprint] [journal] [video] [video] [course] [review]
Bennett and Stinespring, together at last
C. Heunen and R. Kaarsgaard
Quantum Physics and Logic, EPTCS 343:102-118, 2021
[preprint] [proceedings] [video]
Tensor-restriction categories
C. Heunen and J. S. Pacaud Lemay
Theory and Applications of Categories 37(21):635-670, 2021
[preprint] [journal] [review] [review]
Weakly measured while loops: peeking at quantum states
P. Andres-Martinez and C. Heunen
Quantum Science and Technology 7:025007, 2022
[preprint] [journal] [video] [poster]
Compact inverse categories
R. Cockett and C. Heunen
Logic and Structure in Computer Science and Beyond, Outstanding Contributions to Logic 25:813-832, 2023
[preprint] [book]
Monoidal characterisation of groupoids and connectors
M. Gran, C. Heunen, and S. Tull
Topology and its Applications, 106966, 2019
[preprint] [journal] [review]
Ontological models for quantum theory as functors
A. Gheorghiu and C. Heunen
Quantum Physics and Logic, EPTCS 318:196-212, 2020
[preprint] [proceedings]
Topos quantum theory with short posets
J. Harding and C. Heunen
Order 38:111-125, 2021
[preprint] [journal] [review]
Automated distribution of quantum circuits
P. Andres Martinez and C. Heunen
Physical Review A 100:032308, 2019
[preprint] [journal]
Tensor topology
P. Enrique Moliner, C. Heunen, and S. Tull
Journal of Pure and Applied Algebra 224(10):106378, 2020
[preprint] [journal] [review]
Limits in dagger categories
C. Heunen and M. Karvonen
Theory and Applications of Categories 34(18):468-513, 2019
[preprint] [journal] [review] [review]
Boolean subalgebras of orthoalgebras
J. Harding, C. Heunen, Bert Lindenhovius, and M. Navara
Order 36(3):563--609, 2019
[preprint] [journal] [review] [review]
Reversible effects as inverse arrows
C. Heunen, R. Kaarsgaard and M. Karvonen
Mathematical Foundations of Programming Semantics, ENTCS 341:179-199, 2018
[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.
[preprint] [proceedings]
Purity through factorisation
O. Cunningham and C. Heunen
(EPTCS 266:315-328) proceedings of Quantum Physics and Logic, 2017.
[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.
[preprint] [proceedings]
Frobenius structures over Hilbert C*-modules
C. Heunen and M. L. Reyes
Communications in Mathematical Physics 361(2):787--824, 2018
[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.
[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.
[preprint] [journal]
Discretization of C*-algebras
C. Heunen and M. L. Reyes
Journal of Operator Theory 77(1):19-37, 2017
[preprint] [journal] [review]
Pictures of complete positivity in arbitrary dimension
B. Coecke and C. Heunen
Information and Computation 250:50-58, 2016
[preprint] [journal] [review]
(EPTCS 95:27-35) in the proceedings of Quantum Physics and Logic VIII, 2011
[preprint] [proceedings]
The CBH characterisation theorem beyond algebraic quantum theory
C. Heunen and A. Kissinger
Information and Computation 285(B):104828, 2021
[preprint] [journal] [review]
Monads on dagger categories
C. Heunen and M. Karvonen
Theory and Applications of Categories 31(35):1016-1043, 2016
[preprint] [journal] [review] [review]
Reversible monadic programming
(ENTCS 319:217--237) proceedings of Mathematical Foundations of Programming Semantics, 2015
[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
[preprint] [proceedings]
The category of matroids
C. Heunen and V. Patta
Applied Categorical Structures 26(2):205-237, 2017.
[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
[preprint] [proceedings] [review]
Axiomatizing complete positivity
O. Cunningham and C. Heunen
(EPTCS 195:148--157) In the proceedings of Quantum Physics and Logic, 2015
[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
[preprint] [proceedings]
Mathematical Structures in Computer Science, 29(7):972--1006, 2019
[preprint] [journal]
The many classical faces of quantum structures
C. Heunen
Entropy 19(4):144, 2017.
[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
[preprint] [proceedings]
Categories of quantum and classical channels
B. Coecke, C. Heunen, and A. Kissinger
Quantum Information Processing 15(12):5179--5209, 2016
[preprint] [journal]
(EPTCS 158:1-14) in the proceedings of Quantum Physics and Logic IX, 2012
[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
[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
[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
[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
[preprint] [proceedings]
Characterizations of categories of commutative C*-subalgebras
C. Heunen
Communications in Mathematical Physics 331(1):215-238, 2014
[preprint] [journal] [review]
Quantum realization of arbitrary joint measurability structures
R. Kunjwal, C. Heunen, and T. Fritz
Physical Review A 89(5):052126, 2014
[preprint] [journal]
Active lattices determine AW*-algebras
C. Heunen and M. L. Reyes
Journal of Mathematical Analysis and Applications 416:289-313, 2014
[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
[preprint] [journal]
Matrix multiplication is determined by orthogonality and trace
C. Heunen and D. Horsman
Linear Algebra and its Applications 439(12):4130-4134, 2013
[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
[preprint] [proceedings]
On the functor l2
C. Heunen
Computation, Logic, Games, and Quantum Foundations: 107-121, 2013
[preprint] [book] [erratum]
Compositional quantum logic
B. Coecke, C. Heunen, and A. Kissinger
Computation, Logic, Games, and Quantum Foundations: 21-36, 2013
[preprint] [book] [review]
Diagonalizing matrices over AW*-algebras
C. Heunen and M. L. Reyes
Journal of Functional Analysis 264(8):1873-1898, 2013
[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
[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
[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
[preprint] [book] [review] [review]
Entangled and sequential quantum protocols with dephasing
S. Boixo and C. Heunen
Physical Review Letters 108:120402, 2012
[preprint] [journal]
Complementarity in categorical quantum mechanics
C. Heunen
Foundations of Physics 42(7): 856--873, 2012
[preprint] [journal] [review]
Noncommutativity as a colimit
B. van den Berg and C. Heunen
Applied Categorical Structures 20(4):393--414, 2012
[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
[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
[preprint] [journal] [review] [review]
Bohrification
C. Heunen, N.P. Landsman, and B. Spitters
chapter in "Deep Beauty" (editor: H. Halvorson), 2011
[preprint] [book] [review] [review]
Quantum logic in dagger kernel categories
C. Heunen and B. Jacobs
Order 27(2):177-212, 2010
[preprint] [journal] [review]
(ENTCS 270(2):79-103) in the proceedings of Quantum Physics and Logic VI, 2009
[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
[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
[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
[journal] [review]
An embedding theorem for Hilbert categories
C. Heunen
Theory and Applications of Categories 22(13):321-344, 2009
[preprint] [journal]
Semimodule enrichment
C. Heunen
(ENTCS 218:193-208) in the proceedings of MFPS XXIV, 2008
[proceedings]
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
[discussion] [preprint] [proceedings]
Arrows, like Monads, are Monoids
C. Heunen and B. Jacobs
(ENTCS 158:219-236) in the proceedings of MFPS 22, 2006
[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]