Quantum-to-classical transition via quantum cellular automata

• URL: http://arxiv.org/abs/2012.04237v4
• Date: Sun, 1 Aug 2021 17:19:27 GMT
• Title: Quantum-to-classical transition via quantum cellular automata
• Authors: Pedro C.S. Costa
• Abstract summary: A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems. We show that the emergent-effective result of the former microscopic discrete model converges to the diffusion equation and to a classical transport equation.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

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