Finite dimensional Hilbert spaces are complete for dagger compact closed categories

Peter Selinger - Finite dimensional Hilbert spaces are complete for dagger compact closed categories

lmcs:1086 - Logical Methods in Computer Science, August 10, 2012, Volume 8, Issue 3 - https://doi.org/10.2168/LMCS-8(3:6)2012

Finite dimensional Hilbert spaces are complete for dagger compact closed categoriesArticle

Authors: Peter Selinger

We show that an equation follows from the axioms of dagger compact closed categories if and only if it holds in finite dimensional Hilbert spaces.

Volume: Volume 8, Issue 3

Published on: August 10, 2012

Imported on: March 22, 2011

Keywords: Mathematics - Category Theory, Quantum Physics, F.3.2, F.4.1

Funding:

Source : OpenAIRE Graph

Mathematics Subject Classification 2020¹

Sources:

Filippo Bonchi;Alessandro Di Giorgio;Alessio Santamaria, 2023, Deconstructing the Calculus of Relations with Tape Diagrams, Proceedings of the ACM on Programming Languages, 7, POPL, pp. 1864-1894, 10.1145/3571257, https://doi.org/10.1145/3571257.

Christian Herrmann, 2021, On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices, Algebra Universalis, 83, 1, 10.1007/s00012-021-00760-3, https://doi.org/10.1007/s00012-021-00760-3.

Robin Kaarsgaard, 2019, Inversion, Iteration, and the Art of Dual Wielding, arXiv (Cornell University), pp. 34-50, 10.1007/978-3-030-21500-2_3, http://arxiv.org/abs/1904.01679.

Holger Bock Axelsen;Robin Kaarsgaard, 2016, Join Inverse Categories as Models of Reversible Recursion, Lecture notes in computer science, pp. 73-90, 10.1007/978-3-662-49630-5_5.

Jennifer Chubb;Valentina Harizanov, 2016, A (very) brief tour of quantum mechanics, computation, and category theory, Cambridge University Press eBooks, pp. 8-22, 10.1017/cbo9781139519687.003.

Robin Kaarsgaard;Holger Bock Axelsen;Robert Glück, 2016, Join inverse categories and reversible recursion, Journal of Logical and Algebraic Methods in Programming, 87, pp. 33-50, 10.1016/j.jlamp.2016.08.003.

Chris Heunen;Sean Tull, 2015, Categories of relations as models of quantum theory, Electronic Proceedings in Theoretical Computer Science, 195, pp. 247-261, 10.4204/eptcs.195.18, https://doi.org/10.4204/eptcs.195.18.

Jort Martinus Bergfeld;Joshua Sack, 2015, Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs, Soft Computing, 21, 6, pp. 1421-1441, 10.1007/s00500-015-1802-6, https://doi.org/10.1007/s00500-015-1802-6.

Svatopluk Krýsl, 2015, Elliptic complexes over C∗-algebras of compact operators, arXiv (Cornell University), 101, pp. 27-37, 10.1016/j.geomphys.2015.12.001, http://arxiv.org/abs/1506.06244.

André Ranchin;Bob Coecke, 2014, Complete set of circuit equations for stabilizer quantum mechanics, arXiv (Cornell University), 90, 1, 10.1103/physreva.90.012109, http://arxiv.org/abs/1310.7932.

Richard Blute;Marc Comeau, 2014, Von Neumann Categories, Applied Categorical Structures, 23, 5, pp. 725-740, 10.1007/s10485-014-9375-6.

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