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Foundations of Physics

, Volume 41, Issue 3, pp 564–579 | Cite as

Properties of QBist State Spaces

  • D. M. Appleby
  • Åsa Ericsson
  • Christopher A. Fuchs
Article

Abstract

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication (Fuchs and Schack, arXiv:0906.2187v1, 2009) advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset—quantum-state space—might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in Fuchs and Schack (arXiv:0906.2187v1, 2009), and all in conformity with quantum theory.

Keywords

Quantum-state space SIC-POVM Bayesian Interpretation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • D. M. Appleby
    • 1
  • Åsa Ericsson
    • 1
  • Christopher A. Fuchs
    • 1
  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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