Generalised compositional theories and diagrammatic reasoning

Bob Coecke, Ross Duncan, Aleks Kissinger, Quanlong Wang

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Abstract

This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.
LanguageEnglish
Title of host publicationQuantum Theory
Subtitle of host publicationInformational Foundations and Foils
Editors Giulio Chiribella, Robert W. Spekkens
Place of PublicationNetherlands
PublisherSpringer
Pages1-55
Number of pages55
Volume181
Edition1
ISBN (Print)9789401773027
Publication statusPublished - 11 Jun 2015

Publication series

NameFundamental Theories of Physics
PublisherSpringer Netherlands
No.1
Volume181
ISSN (Print)0168-1222

Fingerprint

calculus
quantum theory

Keywords

  • quantum physics
  • quantum theory
  • theoretical physics
  • quantum mechanics

Cite this

Coecke, B., Duncan, R., Kissinger, A., & Wang, Q. (2015). Generalised compositional theories and diagrammatic reasoning. In G. Chiribella, & R. W. Spekkens (Eds.), Quantum Theory: Informational Foundations and Foils (1 ed., Vol. 181, pp. 1-55). (Fundamental Theories of Physics; Vol. 181, No. 1). Netherlands: Springer.
Coecke, Bob ; Duncan, Ross ; Kissinger, Aleks ; Wang, Quanlong. / Generalised compositional theories and diagrammatic reasoning. Quantum Theory: Informational Foundations and Foils. editor / Giulio Chiribella ; Robert W. Spekkens. Vol. 181 1. ed. Netherlands : Springer, 2015. pp. 1-55 (Fundamental Theories of Physics; 1).
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Coecke, B, Duncan, R, Kissinger, A & Wang, Q 2015, Generalised compositional theories and diagrammatic reasoning. in G Chiribella & RW Spekkens (eds), Quantum Theory: Informational Foundations and Foils. 1 edn, vol. 181, Fundamental Theories of Physics, no. 1, vol. 181, Springer, Netherlands, pp. 1-55.

Generalised compositional theories and diagrammatic reasoning. / Coecke, Bob; Duncan, Ross; Kissinger, Aleks; Wang, Quanlong.

Quantum Theory: Informational Foundations and Foils. ed. / Giulio Chiribella; Robert W. Spekkens. Vol. 181 1. ed. Netherlands : Springer, 2015. p. 1-55 (Fundamental Theories of Physics; Vol. 181, No. 1).

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

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N2 - This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.

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Coecke B, Duncan R, Kissinger A, Wang Q. Generalised compositional theories and diagrammatic reasoning. In Chiribella G, Spekkens RW, editors, Quantum Theory: Informational Foundations and Foils. 1 ed. Vol. 181. Netherlands: Springer. 2015. p. 1-55. (Fundamental Theories of Physics; 1).