Information Dimension of Dissipative Quantum Walks

We study the temporal growth of the von Neumann entropy for dissipative quantum walks on networks. By using a phenomenological quantum master equation, the quantum stochastic walk (QSW), we are able to parametrically scan the crossover from purely coherent quantum walks to purely diffusive random wa...

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Published in:arXiv.org 2014-08
Main Authors: Schijven, P, Muelken, O
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Language:English
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Computer simulation
Crossovers
Economic models
Entropy
Random walk
Random walk theory
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description We study the temporal growth of the von Neumann entropy for dissipative quantum walks on networks. By using a phenomenological quantum master equation, the quantum stochastic walk (QSW), we are able to parametrically scan the crossover from purely coherent quantum walks to purely diffusive random walks. In the latter limit the entropy shows a logarithmic growth, which is proportional to the information dimension of the random walk on the network. Here we present results for the von Neumann entropy based on the reduced density operator of the QSW. It shows a similar logarithmic growth for a wide range of parameter values and networks. As a consequence, we propose the logarithmic growth rate of the von Neumann entropy to be a natural extension of the information dimension to dissipative quantum systems. We corroborate our results by comparing to numerically exact simulations.
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subjects Computer simulation
Crossovers
Economic models
Entropy
Random walk
Random walk theory
title Information Dimension of Dissipative Quantum Walks
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