title: Structure of reversible computation determines the self-duality of quantum theory.
abstract: Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory, however, both notions are in some sense identical: outcome probabilities are given by the overlap between two state vectors--quantum theory is self-dual. In this Letter, we show that this notion of self-duality can be understood from a dynamical point of view. We prove that self-duality follows from a computational primitive called bit symmetry: every logical bit can be mapped to any other logical bit by a reversible transformation. Specifically, we consider probabilistic theories more general than quantum theory, and prove that every bit-symmetric theory must necessarily be self-dual. We also show that bit symmetry yields stronger restrictions on the set of allowed bipartite states than the no-signalling principle alone, suggesting reversible time evolution as a possible reason for limitations of nonlocality.
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada.
authors.forename: Markus P
authors.initials: MP
authors.lastname: Müller
authors.forename: Cozmin
authors.initials: C
authors.lastname: Ududec