Quantum Probabilities: An Information-Theoretic Interpretation∗

This Chapter develops a realist information-theoretic interpretation of the non-classical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that information in the physical sense has new structural features, just as the transition from clas-sical to relativistic physics rests on the recognition that space-time is structurally different than we thought. Hilbert space, the event space of quantum systems, is interpreted as a kinematic (i.e., pre-dynamic) framework for an indeterministic physics, in the sense that the geometric structure of Hilbert space imposes objective probabilistic or information-theoretic constraints on correlations between events, just as the geometric structure of Minkowski space in special relativity imposes spatio-temporal kinematic constraints on events. The interpretation of quantum probabilities is more subjectivist in spirit than other discussions in this book (e.g., the chapter by Timpson), insofar as the quantum state is interpreted as a credence function—a bookkeeping device for keeping track of probabilities—but it is also objective (or intersubjective), insofar as the credences specified by the quantum state are understood as uniquely determined, via Gleason’s theorem, by objective correlational constraints on events in the nonclassical quantum event space defined by the subspace structure of Hilbert space.