PIRSA:18040114

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

APA

(2018). Symmetric Informationally Complete Measurements Identify the Essential Difference between Classical and Quantum. Perimeter Institute for Theoretical Physics. https://pirsa.org/18040114

MLA

Symmetric Informationally Complete Measurements Identify the Essential Difference between Classical and Quantum. Perimeter Institute for Theoretical Physics, Apr. 10, 2018, https://pirsa.org/18040114

BibTex

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2018},
            month = {apr},
            note = {PIRSA:18040114 see, \url{https://scivideos.org/index.php/pirsa/18040114}}
          }
          
Talk numberPIRSA:18040114
Talk Type Conference

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.