# Quantum-Bayesian Coherence

@article{Fuchs2009QuantumBayesianC, title={Quantum-Bayesian Coherence}, author={Christopher A. Fuchs and R. Schack}, journal={arXiv: Quantum Physics}, year={2009} }

In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, we show how to view the Born Rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign… Expand

#### 236 Citations

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#### References

SHOWING 1-10 OF 274 REFERENCES

A Quantum-Bayesian Route to Quantum-State Space

- Mathematics, Physics
- 2011

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… Expand

Subjective probability and quantum certainty

- Computer Science, Physics
- 2006

This paper investigates the concept of certainty in quantum mechanics and gives a version of an argument of Stairs, which applies the Kochen–Specker theorem to an entangled bipartite system. Expand

Probabilistic Theories: What Is Special about Quantum Mechanics?

- 2008

Quantum Mechanics (QM) is a very special probabilistic theory, yet we don’t know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical… Expand

QBism, the Perimeter of Quantum Bayesianism

- Mathematics, Physics
- 2010

This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian… Expand

Philosophy of Quantum Information and Entanglement: Probabilistic theories: What is special about Quantum Mechanics?

- Physics, Mathematics
- 2010

Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical… Expand

Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference

- Mathematics
- 2011

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Classical probability theory is independent of… Expand

Objective Probability and Quantum Fuzziness

- Mathematics, Physics
- 2009

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations… Expand

A remark on Fuchs' bayesian interpretation of quantum mechanics

- Physics
- 2008

Abstract Quantum mechanics is a theory whose foundations spark controversy to this day. Although many attempts to explain the underpinnings of the theory have been made, none has been unanimously… Expand

Quantum Bayesianism: A study

- Physics
- 2008

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is… Expand

Unknown Quantum States and Operations, a Bayesian View

- Computer Science, Physics
- 2004

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. Expand