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- Title
Quantum-to-classical transition via quantum cellular automata.
- Authors
Costa, Pedro C. S.
- Abstract
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here, we propose a simple coarse-graining map, where the spatial structure of the QCA is merged into effective ones. Starting with a QCA that simulates the Dirac equation, we apply this coarse-graining map recursively until we get its effective dynamics in the semiclassical limit, which can be described by a classical cellular automaton. We show that the emergent-effective result of the former microscopic discrete model converges to the diffusion equation and to a classical transport equation under a specific initial condition. Therefore, QCA is a good model to validate the quantum-to-classical transition.
- Subjects
CELLULAR automata; QUANTUM transitions; TRANSPORT equation; HEAT equation; DIRAC equation; SEMICLASSICAL limits
- Publication
Quantum Information Processing, 2021, Vol 20, Issue 7, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-021-03175-0