PIRSA:09080015 Conference Quantum Foundations

DOI10.48660/09080015

Conference/School: Reconstructing Quantum Theory - 2009

Wilce, A. (2009). Four and a Half Axioms for Quantum Mechanics. Perimeter Institute. https://pirsa.org/09080015

Wilce, Alexander. Four and a Half Axioms for Quantum Mechanics. Perimeter Institute, Aug. 13, 2009, https://pirsa.org/09080015 

@misc{ pirsa_PIRSA:09080015,
  doi = {10.48660/09080015},
  url = {https://pirsa.org/09080015},
  author = {Wilce, Alexander},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Four and a Half Axioms for Quantum Mechanics},
  publisher = {Perimeter Institute},
  year = {2009},
  month = {aug},
  note = {PIRSA:09080015 see, \url{https://pirsa.org}}
}

Abstract

I will discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. These require that systems appear completely classical as restricted to a single measurement, that different measurements, and likewise different pure states, be equivalent up to the action of a compact group of symmetries, and that every state be the marginal of a bipartite state perfectly correlating two measurements. This much yields a mathematical representation of measurements, states and symmetries that is already very suggestive of quantum mechanics. One final postulate (a simple minimization principle, still in need of a clear interpretation) forces the theory's state space to be that of a formally real Jordan algebra

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