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math.CTOct 1, 2011
36
citations (OpenAlex)
authors
  • Bob Coecke
  • Chris Heunen
institutions
  • University of Edinburgh
  • University of Oxford
arXiv abstractPDF
paper

Pictures of complete positivity in arbitrary dimension

arXiv:1110.3055 · doi:10.1016/j.ic.2016.02.007

Abstract

Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CP-construction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension. Second, we axiomatize when a given category is the result of this construction.

Final version

References in corpus (4)

  • Quantum Logic in Dagger Kernel Categories
  • Categories for the practising physicist
  • A Diagrammatic Approach to Quantum Dynamics
  • Compactly accessible categories and quantum key distribution

Cited by in corpus (12)

  • The algebra of entanglement and the geometry of composition
  • Reconstructing quantum theory from diagrammatic postulates
  • Reversible effects as inverse arrows
  • A Bestiary of Sets and Relations
  • The ZX&-calculus: A complete graphical calculus for classical circuits using spiders
  • Purity through Factorisation
  • Coend Optics for Quantum Combs
  • Dagger linear logic for categorical quantum mechanics
  • Categories of Quantum and Classical Channels (extended abstract)
  • Quantum Darwinism and the spreading of classical information in non-classical theories
  • Effectuses in Categorical Quantum Foundations
  • Some graphical aspects of Frobenius structures
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