Properties of quantum stochastic walks from the Hurst exponent

This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i.e. unitary quantum walks. Our main goal is to present a measure of coherence of the walk. To this end, we utilize the Hurst exponent. As the quantum stochastic walk model encompasses both classical random walks and quantum walks, we are interested how the continuous change from one regime to the other influences the Hurst exponent. Moreover this model allows for behavior which is not found in any of the previously mentioned model -- the model with global dissipation. We derive the probability distribution for the walker, and determine the Hurst exponent analytically, showing that ballistic regime of the walk is maintained even at large dissipation strength.