Oscar C. O. Dahlsten, Andrew J. P. Garner, Vlatko Vedral
In this paper we introduce an operational physical locality principle, branch locality, similar to non-signaling but applicable to single systems. Branch locality restricts the dynamics that can be implemented in a spatial interferometer. We give a simple proof that any theory with state-changing dynamics either: (i) respects a particular uncertainty relation, or (ii) violates branch locality. Quantum theory and classical theory are in category (i), whereas category (ii) includes the theory known as box world. Box world is typically presented as reasonable because it satisfies the non-signaling condition, but here we demonstrate that if it is allowed non-trivial dynamics, it must violate a locality principle that any physical theory should respect. Our results hence present a compelling argument for the necessity of the uncertainty relation in quantum and post-quantum theories.
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http://arxiv.org/abs/1206.5702
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