Thermodynamics of N-dimensional quantum walks

Abstract

The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-position initial state, and a separable one. The resulting entanglement temperature is presented as function of the parameters of the system and those of the initial conditions.

arXiv comment10 pages, 4 figs

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• Transient temperature and mixing times of quantum walks on cycles
• Steepest Entropy Ascent Solution for a Continuous-Time Quantum Walker
• Analytical expression for variance of homogeneous-position quantum walk with decoherent position
• Zero Range Process and Multi-Dimensional Random Walks