Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule

@article{Wallace2003QuantumPF,
  title={Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule},
  author={D. Wallace},
  journal={Studies in History and Philosophy of Modern Physics},
  year={2003},
  volume={38},
  pages={311-332}
}
  • D. Wallace
  • Published 18 December 2003
  • Computer Science
  • Studies in History and Philosophy of Modern Physics
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158 Citations
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158 Citations

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References

SHOWING 1-10 OF 50 REFERENCES
Quantum probability from decision theory?
In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical…
Quantum theory of probability and decisions
  • D. Deutsch
  • Philosophy, Physics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1999
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions…
On an argument of David Deutsch
We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that…
Derivation of the Born rule from operational assumptions
  • S. Saunders
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2004
TLDR
The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state, and provides a probability rule for state spaces that are not Hilbert spaces.
Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation
Understanding Deutsch's probability in a deterministic multiverse
How probability arises in quantum mechanics
What is Probability
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics:…
Quantum Theory Needs No ‘Interpretation’
Purpose of this article is to stress the fact that Quantum Theory does not need an interpretation other than being an algorithm for computing probabilities associated with macroscopic phenomena and…
Implications of quantum theory in the foundations of statistical mechanics
An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a…
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