Structure of Reversible Computation Determines the Self-Duality of Quantum Theory

Markus P. Müller and Cozmin Ududec
Phys. Rev. Lett. 108, 130401 – Published 27 March 2012

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.

  • Figure
  • Received 6 January 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.130401

© 2012 American Physical Society

Authors & Affiliations

Markus P. Müller and Cozmin Ududec

  • Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada

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Vol. 108, Iss. 13 — 30 March 2012

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