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Foundations of Physics

, Volume 41, Issue 3, pp 345–356 | Cite as

A Quantum-Bayesian Route to Quantum-State Space

  • Christopher A. Fuchs
  • Rüdiger Schack
Article

Abstract

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.

Keywords

Quantum foundations Quantum state space Quantum Bayesianism Born rule Bayesian 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Department of Mathematics, Royal HollowayUniversity of LondonEgham, SurreyUK

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