Symmetric Informationally Complete Measurements Identify the Essential Difference between Classical and Quantum

          @misc{ pirsa_PIRSA:18040114,
            doi = {10.48660/18040114},
            url = {https://pirsa.org/18040114},
            author = {},
            keywords = {},
            language = {en},
            title = {Symmetric Informationally Complete Measurements Identify the Essential Difference between Classical and Quantum},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {apr},
            note = {PIRSA:18040114 see, \url{https://pirsa.org}}
          }
          

Abstract

In this talk we describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) with a probabilistic representation of quantum theory. Towards this, we make use of the idea that the Born Rule is a consistency criterion among subjectively assigned probabilities rather than a tool to set purely physically mandated probabilities. In our setting, the difference between quantum theory and classical statistical physics is the way their physical assumptions augment bare probability theory: Classical statistical physics corresponds to a trivial augmentation, while quantum theory makes crucial use of the Born Rule. We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes the distinction between the two theories in at least two senses, one functional, the other geometric. Our results suggest that this representation supplies a natural vantage point from which to identify their essential differences, and, perhaps thereby, a set of physical postulates reflecting the quantum nature of the world.