Cellular automata in operational probabilistic theories
arXiv:1911.11216 · doi:10.22331/q-2020-07-09-294
Abstract
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite systems. The notion of causal influence is introduced, and its relation with the usual property of signalling is discussed. We then introduce homogeneity, namely the property of an update rule to evolve every system in the same way, and prove that systems evolving by a homogeneous rule always correspond to vertices of a Cayley graph. Next, we define the notion of locality for update rules. Cellular automata are then defined as homogeneous and local update rules. Finally, we prove a general version of the wrapping lemma, that connects CA on different Cayley graphs sharing some small-scale structure of neighbourhoods.
Updated version: the only change consists in the extension of the proof of lemma 2
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Cited by in corpus (10)
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- Classicality without local discriminability: decoupling entanglement and complementarity
- Incompatibility of observables, channels and instruments in information theories
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- Shannon theory beyond quantum: information content of a source
- Causal influence in operational probabilistic theories
- Renormalisation of Quantum Cellular Automata
- Minimal operational theories: classical theories with quantum features
- Causal influence versus signalling for interacting quantum channels