A Quantum-Bayesian Route to Quantum-State Space

@article{Fuchs2011AQR,
  title={A Quantum-Bayesian Route to Quantum-State Space},
  author={Christopher A. Fuchs and R. Schack},
  journal={Foundations of Physics},
  year={2011},
  volume={41},
  pages={345-356}
}
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… 
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References

SHOWING 1-10 OF 40 REFERENCES
Quantum-Bayesian Coherence
TLDR
It is argued that the Born Rule should be seen as an empirical addition to Bayesian reasoning itself, and how to view it as a normative rule in addition to usual Dutch-book coherence is shown.
Unknown Quantum States and Operations, a Bayesian View
TLDR
Two results are motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: a definetti theorem for quantum states and a de Fintti theorem forquantum operations.
Subjective probability and quantum certainty
Unknown Quantum States: The Quantum de Finetti Representation
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the…
Quantum Bayesianism: A study
Properties of QBist State Spaces
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 Bayes rule
We state a quantum version of Bayes’s rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on…
Quantum Mechanics as Quantum Information (and only a little more)
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion…
Quantum mechanics without probability amplitudes
First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are…
Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of…
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