A Dynamic-Logical Perspective on Quantum Behavior

In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and inter-pret quantum behavior. Our main thesis is that all the non-classical prop-erties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum mea-surements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators pre-viously used to model various forms of classical information flow: the “test ” operator from Dynamic Logic, the “announcement ” operator from Dynamic Epistemic Logic and the “revision ” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics ” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static ” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system