Chris Heunen

Chris Heunen

EPSRC Research Fellow
Lecturer at St Hugh's College

University of Oxford
Department of Computer Science, Room 213
Wolfson Building, Parks Road, Oxford OX1 3QD

heunen(at)cs.ox.ac.uk

Curriculum vitae

Teaching

I teach the undergraduate course Logic and Proof and the graduate course Categorical Quantum Mechanics, as well as tutor at St Hugh's College, and supervise PhD students Hugo Nava Kopp, Vaia Patta, Oscar Cunningham, and Sean Tull.

Research

I work in quantum computer science, more precisely on the mathematical foundations of physics, especially quantum mechanics, and its logical aspects. My weapons of choice are category theory, functional analysis, and order theory; specifically, monoidal categories, operator algebras, and orthomodular lattices. I suppose you could say that my ultimate goal is to really understand the category of Hilbert spaces, in particular categorical aspects of a choice of basis.

For a very gentle introduction to the ideas behind my work, see "The state of quantum computer science".

Publications

Type: Book Journal Proceedings Chapter Other
Year:
Total:
Book review: Foundations of relational realism
M. Epperson and E. Zafiris
Studies in History and Philosophy of Modern Physics, 2014
[journal]
Mixed quantum states in higher categories
C. Heunen, J. Vicary, and L. Wester
to appear in the proceedings of Quantum Physics and Logic XI, 2014
[pdf] [preprint]
Categories of quantum and classical channels
B. Coecke, C. Heunen, and A. Kissinger
[pdf] [preprint] [journal]
Extending obstructions to noncommutative functorial spectra
B. van den Berg and C. Heunen
[pdf] [preprint] [journal]
Operational theories and categorical quantum mechanics
S. Abramsky and C. Heunen
to appear in Lecture Notes in Logic: Logic and algebraic structures in quantum computing and information
Association for Symbolic Logic and Cambridge University Press, 2014
[pdf] [preprint]
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
[pdf] [preprint] [journal]
All joint measurability structures are quantum realizable
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. Reyes
[pdf] [preprint] [journal]
Quantum theory realises all joint measurability graphs
C. Heunen, T. Fritz, and M. 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
to appear in the proceedings of Quantum Physics and Logic X, 2013
[pdf] [preprint]
On the functor l2
C. Heunen
[pdf] [preprint] [book]
Compositional quantum logic
B. Coecke, C. Heunen, and A. Kissinger
[pdf] [preprint] [book]
Diagonalizing matrices over AW*-algebras
C. Heunen and M. Reyes
Journal of Functional Analysis 264(8):1873-1898, 2013
[pdf] [preprint] [journal] [review]
Relative Frobenius algebras are groupoids
[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]
Categories of quantum and classical channels (extended abstract)
B. Coecke, C. Heunen, and A. Kissinger
(EPTCS 158:1-14) in the proceedings of Quantum Physics and Logic IX, 2012
[pdf] [preprint] [proceedings]
Pictures of complete positivity in arbitrary dimension
B. Coecke and C. Heunen
(EPTCS 95:27-35) in the proceedings of Quantum Physics and Logic VIII, 2011
[pdf] [preprint] [proceedings]
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]
No-go theorems for functorial localic spectra of noncommutative rings
B. van den Berg and C. Heunen
(EPTCS 95:21-25) 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
[pdf] [preprint] [book] [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]
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
[pdf] [preprint] [journal] [review]
Bohrification
C. Heunen, N.P. Landsman, and B. Spitters
chapter in "Deep Beauty" (editor: H. Halvorson), 2011
[pdf] [preprint] [book] [review]
Quantum logic in dagger kernel categories
C. Heunen and B. Jacobs
Order 27(2):177-212, 2010
[pdf] [preprint] [journal] [review]
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
Foundations of Physics, 39(7):731-759, 2009
[pdf] [preprint] [journal] [review]
Quantum logic in dagger kernel categories
C. Heunen and B. Jacobs
(ENTCS 270(2):79-103) in the proceedings of Quantum Physics and Logic VI, 2009
[pdf] [preprint] [proceedings]
A topos for algebraic quantum theory
C. Heunen, N.P. Landsman, and B. Spitters
[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
[pdf] [publisher] [hardcopies available on request] [presentation: slides, text]
Categorical semantics for Arrows
B. Jacobs, C. Heunen, and I. Hasuo
[pdf] [journal] [review]
An embedding theorem for Hilbert categories
C. Heunen
[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
[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]