Distributed Probabilistic and Quantum Strategies

Abstract

Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copy-cat strategies as identities. A higher-order probabilistic process language reminiscent of Milnerʼs CCS is interpretable within probabilistic strategies. W.r.t. a new definition of quantum event structure, it is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure. This gives a non-traditional take on the consistent-histories approach to quantum theory. It leads to an extension to quantum strategies. Probabilistic games extend to games with payoff, symmetry and games of imperfect information.