Constructor theory of probability.
Unitary quantum theory, having no Born Rule, isnon-probabilistic. Hence the notorious problem of reconciling it with theunpredictabilityandappearance of stochasticityin quantum measurements. Generalizing and improving upon the so-called 'decision-theoretic approach', I shall recast that problem in the recently proposedconstructor theory of information-where quantum theory is represented as one of a class ofsuperinformation theories, which arelocal,non-probabilistictheories 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 sufficientconditionsfor a superinformation theory to inform decisions (made under it)as ifit were probabilistic, via a Deutsch-Wallace-type argument-thus defining a class ofdecision-supportingsuperinformation 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 fromphysical propertiesexpressed by constructor-theoretic principles.
Department of Materials , University of Oxford , Oxford , UK.
Chiara
0000-0002-2690-4433
C
Marletto
Born Rule; constructor theory; probability; quantum physics