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11 - Quantum Foundations

Published online by Cambridge University Press:  30 March 2017

Bob Coecke
Affiliation:
University of Oxford
Aleks Kissinger
Affiliation:
Radboud Universiteit Nijmegen
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Summary

Mermin once summarized a popular attitude towards quantum theory as ‘Shut up and calculate.’ We suggest a different slogan: ‘Shut up and contemplate!’

Lucien Hardy and Rob Spekkens, 2010

This chapter is dedicated to the foundations of quantum theory, or as it's more fashionably called these days, quantum foundations. Here, we will use all of the things we've learned so far to probe some very deep questions:

  1. 1. What features of nature are imposed on us by quantum theory?

  2. 2. Conversely, what features of a physical theory are imposed on us by (our current understanding of) nature?

  3. 3. Which of these features are ‘properly quantum’, in the sense that they have no counterpart in any classical physical theory?

We'll address these questions by looking at one of those most celebrated (and historically controversial) properties of quantum theory: quantum non-locality. First, we will give a precise definition of non-locality and prove that it exists within the theory of quantum processes and in fact already within the comparatively tiny subtheory of causal Clifford maps. Then, we will present a new process theory called spek, which has locality built right in. A remarkable thing is that the two theories of Clifford maps and spek are identical in every respect except one: the phase group of a single system. And (another spoiler alert!) it is indeed this one difference that kills the proof of non-locality that works for quantum theory.

Quantum Non-locality

Quantum non-locality is probably still the least understood of all the new quantum features, in both philosophical and structural terms. Our upbringing in a seemingly ‘classical’ world, and especially our undeniably corrupting ‘classical’ scientific education, tends to make us expect two things from a physical theory:

  1. 1. Realism: physical systems have real pre-existing properties, and hence the outcome of ‘measuring’ such a property is fixed in some way prior to the measurement.

  2. 2. Locality: it is impossible for one system to affect another distant system instantaneously.

Type
Chapter
Information
Picturing Quantum Processes
A First Course in Quantum Theory and Diagrammatic Reasoning
, pp. 655 - 678
Publisher: Cambridge University Press
Print publication year: 2017

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  • Quantum Foundations
  • Bob Coecke, University of Oxford, Aleks Kissinger, Radboud Universiteit Nijmegen
  • Book: Picturing Quantum Processes
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316219317.012
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  • Quantum Foundations
  • Bob Coecke, University of Oxford, Aleks Kissinger, Radboud Universiteit Nijmegen
  • Book: Picturing Quantum Processes
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316219317.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Quantum Foundations
  • Bob Coecke, University of Oxford, Aleks Kissinger, Radboud Universiteit Nijmegen
  • Book: Picturing Quantum Processes
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316219317.012
Available formats
×