Constructor Theory of Information

TL;DR

This paper introduces a constructor-theoretic framework for understanding information based solely on physical transformations, clarifying fundamental quantum phenomena without circular definitions.

Contribution

It develops a physics-based theory of information that explains quantum phenomena and resolves foundational issues in information theory without relying on prior mathematical assumptions.

Findings

Explains the relationship between classical and quantum information.

Identifies the constructor-theoretic property underlying quantum phenomena.

Clarifies the nature of measurement and entanglement in physical terms.

Abstract

We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are directly about information, independently of the details of particular physical instantiations, it does not regard information as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. It does not suffer from the circularity at the foundations of existing information theory (namely that information and distinguishability are each defined in terms of the other). It explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and entanglement (locally inaccessible information).