Chu spaces: automata with quantum aspects

Abstract

Chu spaces are a model of concurrent computation extending automata theory to express branching time and true concurrency. They exhibit in a primitive form the quantum mechanical phenomena of complementarity and uncertainty. The complementarity arises as the duality of information and time, automata and schedules, and states and events. Uncertainty arises when we define a measurement to be a morphism and notice that increasing structure in the observed object reduces clarity of observation. For a Chu space this uncertainty can be calculated numerically in an attractively simple way directly from its form factor to yield the usual Heisenberg uncertainty relation. Chu spaces correspond to wavefunctions as vectors of Hilbert space, whose inner product operation is realized for Chu spaces as right residuation and whose quantum logic becomes Girard's linear logic.<>