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*> OK, I got interested in this enough to write up a formal note.
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*> Comments welcome.
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*> http://hanson.gmu.edu/bornrule.pdf
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*> Quantum Probability From Decision Theory and Exchangeability
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*> by Robin Hanson, July 27, 2001.
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*> Deutsch's derivation of quantum probability from decision theory has been
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*> criticized as relying on an implausible hidden assumption. I here offer as
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*> a substitute an apparently more plausible exchangeability assumption.
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With his classical representation theorem Bruno De Finetti

showed that a multi-trial probability assignment that is

permutation-symmetric - *exchangeable* - for an arbitrarily

large number of trials, is equivalent to a probability for

the "unknown probabilities".

I wonder whether De Finetti's theorem may have something

to do with "Quantum Probability From Decision Theory and

Exchangeability", or not.

- serafino

----------------------------------------

http://xxx.lanl.gov/abs/quant-ph/0104088

Unknown Quantum States: The Quantum de Finetti Representation

Carlton M. Caves, Christopher A. Fuchs, Ruediger Schack

We present an elementary proof of the quantum de Finetti representation

theorem, a quantum analogue of de Finetti's classical theorem on

exchangeable probability assignments. This contrasts with the original proof

of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies

on advanced mathematics and does not share the same potential for

generalization. The classical de Finetti theorem provides an operational

definition of the concept of an unknown probability in Bayesian probability

theory, where probabilities are taken to be degrees of belief instead of

objective states of nature. The quantum de Finetti theorem, in a closely

analogous fashion, deals with exchangeable density-operator assignments and

provides an operational definition of the concept of an "unknown quantum

state" in quantum-state tomography. This result is especially important for

information-based interpretations of quantum mechanics, where quantum

states, like probabilities, are taken to be states of knowledge rather than

states of nature. We further demonstrate that the theorem fails for real

Hilbert spaces and discuss the significance of this point.

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