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2016 ; 472
(2192
): 20150883
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Constructor theory of probability
#MMPMID27616914
Marletto C
Proc Math Phys Eng Sci
2016[Aug]; 472
(2192
): 20150883
PMID27616914
show ga
Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the
notorious problem of reconciling it with the unpredictability and appearance of
stochasticity in quantum measurements. Generalizing and improving upon the
so-called 'decision-theoretic approach', I shall recast that problem in the
recently proposed constructor theory of information-where quantum theory is
represented as one of a class of superinformation theories, which are local,
non-probabilistic theories conforming to certain constructor-theoretic
conditions. I prove that the unpredictability of measurement outcomes (to which
constructor theory gives an exact meaning) necessarily arises in superinformation
theories. Then I explain how the appearance of stochasticity in (finitely many)
repeated measurements can arise under superinformation theories. And I establish
sufficient conditions for a superinformation theory to inform decisions (made
under it) as if it were probabilistic, via a Deutsch-Wallace-type argument-thus
defining a class of decision-supporting superinformation theories. This broadens
the domain of applicability of that argument to cover constructor-theory
compliant theories. In addition, in this version some of the argument's
assumptions, previously construed as merely decision-theoretic, follow from
physical properties expressed by constructor-theoretic principles.
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