PIRSA:11030086 Scientific Series Quantum Foundations

DOI10.48660/11030086

Series: Quantum Foundations

Müller, M. (2011). From operational axioms to quantum theory - and beyond?. Perimeter Institute. https://pirsa.org/11030086

Müller, Markus. From operational axioms to quantum theory - and beyond?. Perimeter Institute, Mar. 15, 2011, https://pirsa.org/11030086 

@misc{ pirsa_PIRSA:11030086,
  doi = {10.48660/11030086},
  url = {https://pirsa.org/11030086},
  author = {M{\"u}ller, Markus},
  keywords = {Quantum Foundations},
  language = {en},
  title = {From operational axioms to quantum theory - and beyond?},
  publisher = {Perimeter Institute},
  year = {2011},
  month = {mar},
  note = {PIRSA:11030086 see, \url{https://pirsa.org}}
}

Abstract

Usually, quantum theory (QT) is introduced by giving a list of abstract mathematical postulates, including the Hilbert space formalism and the Born rule. Even though the result is mathematically sound and in perfect agreement with experiment, there remains the question of why this formalism is a natural choice, and how QT could possibly be modified in a consistent way. My talk is on recent work with Lluis Masanes, where we show that five simple operational axioms actually determine the formalism of QT uniquely. This is based to a large extent on Lucien Hardy's seminal work. We start with the framework of "general probabilistic theories", a simple, minimal mathematical description for outcome probabilities of measurements. Then, we use group theory and convex geometry to show that the state space of a bit must be a 3D (Bloch) ball, finally recovering the Hilbert space formalism. There will also be some speculation on how to find natural post-quantum theories by dropping one of the axioms.

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