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Properties of QBist State Spaces

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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.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada

    D. M. Appleby, Åsa Ericsson & Christopher A. Fuchs

Authors
  1. D. M. Appleby
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  2. Åsa Ericsson
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  3. Christopher A. Fuchs
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Correspondence to Åsa Ericsson.

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Appleby, D.M., Ericsson, Å. & Fuchs, C.A. Properties of QBist State Spaces. Found Phys 41, 564–579 (2011). https://doi.org/10.1007/s10701-010-9458-7

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  • DOI: https://doi.org/10.1007/s10701-010-9458-7

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