Quantum-Bayesian coherence
Open accessAbstract
In the quantum-Bayesian interpretation of quantum theory (or QBism), 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, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown 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 probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.
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Subjectivistic interpretations such as relational quantum mechanics, QBism, or the approach in ref. 9 are examples of theories that satisfy (Q) and (S) and thus violate (C).
“Another class of examples are subjectivistic interpretations, which regard statements about outcomes of measurements as personal to an agent, such as “relational quantum mechanics”38, “QBism”39,40, or the approach proposed in ref. 9”
From Quantum theory cannot consistently describe the use of itself (2018) · cites this paper as [39]
Interpretations that reject AOE include QBism, the relational interpretation, and the many-worlds interpretation.
“Interpretations that reject AOE include QBism [6, 7], the relational interpretation [5], and the many-worlds interpretation [4].”
From A strong no-go theorem on the Wigner’s friend paradox (2020) · cites this paper as [6]
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- Authors
- Fuchs, C. A., & Schack, R.
- Affiliations
- Perimeter Institute (CA)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2013-12-27
- Volume
- 85
- Issue
- 4
- Pages
- 1693-1715
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2600106234
- Cited by
- 321
- References
- 158
- Citations by year
- 2026: 12 · 2025: 24 · 2024: 11 · 2023: 51 · 2022: 19 · 2021: 25 · 2020: 35 · 2019: 25 · 2018: 21 · 2017: 22 · 2016: 25 · 2015: 16 · 2014: 25 · 2013: 3 · 2012: 5
- FWCI
- 11.84
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- QBism, Born rule, Dutch book argument, coherence, normative rules, Bayesian probability, symmetric informationally complete measurements, quantum state space, measurement outcomes
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