Quantum Probabilities: An Information‐Theoretic Interpretation

Abstract

This Chapter develops a realist information-theoretic interpretation of the nonclassical 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 classical 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.

Unscrambling Subjective and Epistemic Probabilities

“…Itamar himself (2003,2007), Bub (2007Bub ( , 2010 and Fuchs and co-workers have all defended approaches to quantum mechanics in which probabilities are subjective in the sense of being degrees of belief, and some modifications or additions to Bayesian rationality are introduced in order to deal with situations, respectively, in which one deals with 'quantum bets' (incompatible bets possibly with some outcomes in common), in which one assumes nocloning as a fundamental principle, or in which gathering evidence means irreducibly intervening into the world. I take it that all of these authors (as well as de Finetti himself) agree on the assumption that in general there are no present or past facts that will determine the outcomes of quantum bets or any quantum measurements, and thus that the probabilities in their approaches are ontic in the sense used in the previous section.…”

Quantum reaxiomatisations and information-theoretic interpretations of quantum theory

“…As he sees it, quantum theory brings a new information-theoretic structure, which can be regarded as parallel to the Minkowski space-time in special relativity: 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 classical to relativistic physics rests on the recognition that space-time is structurally different from what we thought. (Bub [2011], p. 1).…”

“…In more recent expositions of the information theoretic interpretation, a third line of argument is to be found (Bub and Pitowsky [2010], Bub [2011Bub [ , 2014Bub [ , 2015). The claim is now very explicitly that an information-theoretic interpretation of quantum theory can dissolve the measurement problem, by showing that the problem is, in large part, a 'pseudo-problem'.…”

“…The definite occurrence of a particular event is constrained by the kinematic probabilistic correlations represented by the subspace structure of Hilbert space, and only by these correlations -it is otherwise free. (Bub [2011], p. 23).…”

“…In particular, a research programme gradually developed of trying to reaxiomatise the theory in terms of broadly information-theoretic principles. That this programme might have implications for the traditional conceptual problems and for the interpretation of quantum theory is an idea which has been developed in stages by Jeff Bub, who has argued for what he calls an 'information-theoretic interpretation' of quantum theory (Bub [2000], Clifton et al [2003], Bub [2004Bub [ , 2005, Bub and Pitowsky [2010], Bub [2011Bub [ , 2014Bub [ , 2015). Throughout this work, Bub has been guided by an analogy with Einstein's use of postulates in special relativity.…”