Environment-induced mixing processes in quantum walks
arXiv:1407.2470 · doi:10.1142/S021974991450021X
Abstract
The mixing process of discrete-time quantum walks on one-dimensional lattices is revisited in a setting where the walker is coupled to an environment, and the time evolution of the walker and the environment is unitary. The mixing process is found to be incomplete, in the sense that the walker does not approach the maximally mixed state indefinitely, but the distance to the maximally mixed state saturates to some finite value depending on the size of the environment. The quantum speedup of mixing time is investigated numerically as the size of the environment decreases from infinity to a finite value. The mixing process in this unitary setting can be explained by interpreting it as an equilibration process in a closed quantum system, where subsystems can exhibit equilibration even when the entropy of the total system remains zero.
arXiv comment11 pages. Same as the published version
References in corpus (17)
- Decoherence, einselection, and the quantum origins of the classical
- Average Entropy of a Subsystem
- Quantum mechanical evolution towards thermal equilibrium
- Aspects of generic entanglement
- Decoherence in quantum walks - a review
- Decoherence can be useful in quantum walks
- The quantum to classical transition for random walks
- Open Quantum Random Walks
- Quantum stochastic walks: A generalization of classical random walks and quantum walks
- Quantum speedup of classical mixing processes
- Open Quantum Walks on Graphs
- Complementarity and quantum walks
- Optimal computation with non-unitary quantum walks
- Decoherence in quantum walks and quantum computers
- Statistical dynamics of a non-Abelian anyonic quantum walk
- Anyonic Quantum Walks
- Environment-induced mixing processes in quantum walks