Physics – Quantum Physics
Scientific paper
2011-10-16
Phys. Rev. Lett. 108, 130401 (2012)
Physics
Quantum Physics
4 pages, 1 figure. v2: published version. Title slightly changed, interpretation of Theorem 2 corrected
Scientific paper
10.1103/PhysRevLett.108.130401
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 paper, 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 non-locality.
Mueller Markus P.
Ududec Cozmin
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