On quantum vs. classical probability

          @misc{ pirsa_PIRSA:09010000,
            doi = {10.48660/09010000},
            url = {https://pirsa.org/09010000},
            author = {Rau, Jochen},
            keywords = {Quantum Foundations},
            language = {en},
            title = {On quantum vs. classical probability},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {jan},
            note = {PIRSA:09010000 see, \url{https://pirsa.org}}
          }
          

Abstract

Both classical probability theory and quantum theory lend themselves to a Bayesian interpretation where probabilities represent degrees of belief, and where the various rules for combining and updating probabilities are but algorithms for plausible reasoning in the face of uncertainty. I elucidate the differences and commonalities of these two theories, and argue that they are in fact the only two algorithms to satisfy certain basic consistency requirements. In order to arrive at this result I develop an over-arching framework for plausible reasoning that incorporates both classical probability and quantum theory as special cases.