Quantum Theory: Informational Foundations and Foils

Volume 181 of the series Fundamental Theories of Physics pp 367-420


Post-Classical Probability Theory

  • Howard BarnumAffiliated withDepartment of Physics and Astronomy, University of New MexicoStellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University Email author 
  • , Alexander WilceAffiliated withDepartment of Mathematics, Susquehanna University

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This chapter offers a brief introduction to what is often called the convex-operational approach to the foundations of quantum mechanics, and reviews selected results, mostly by ourselves and collaborators, obtained using that approach. Broadly speaking, the goal of research in this vein is to locate quantum mechanics (henceforth: QM) within a very much more general, but conceptually very straightforward, generalization of classical probability theory. The hope is that, by regarding QM from the outside, so to say, we shall be able to understand it more clearly. And, in fact, this proves to be the case.