Constructor Theory of Information - an overview
Constructor Theory is a new fundamental theory of physics, where everything is expressed solely in terms of possible/impossible tasks. This new mode of explanation was proposed by David Deutsch to replace the prevailing conception of fundamental physics, where everything is expressed solely in terms of initial conditions and laws of motion. The Constructor Theory of Information is one of the first applications of this new approach. This theory of information is expressed solely in terms of which transformations of physical systems are possible and which are impossible—i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Thus information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. For example, by switching to constructor theory one can solve a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. One can also explain the relationship between classical and quantum information, revealing the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, such as 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, unpredictability of deterministic measurement processes, the irreducible perturbation caused by measurement, and locally inaccessible
information (as in entangled systems).