Constructor theory of probability

Journal article

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. Generalising 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.

Authors: Marletto, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Royal Society
• Journal: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
• Volume: 472
• Issue: 2192
• Article number: 20150883
• Publication date: 2016-01-01
• Acceptance date: 2016-07-15
• DOI: 10.1098/rspa.2015.0883
• EISSN: 1471-2946
• ISSN: 1364-5021
• Keywords: constructor theory; probability; quantum physics; Born Rule