Weak Limit of the 3-State Quantum Walk on the Line
arXiv:1404.1330 · doi:10.1103/PhysRevA.90.012307
Abstract
We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time averaged approximation to the PDF found by Inui et. al. to a spatial average of the walk. We show that this smooth approximation constitutes a proper PDF that predicts moments of the real PDF accurately.
8 pages, revtex, for related information see http://www.physics.emory.edu/faculty/boettcher/ v2: minor changes, references added
References in corpus (2)
Cited by in corpus (16)
- Limit distributions of three-state quantum walks: the role of coin eigenstates
- One-Dimensional Coinless Quantum Walks
- Coin dimensionality as a resource in quantum metrology involving discrete-time quantum walks
- Adjustable self-loop on discrete-time quantum walk and its application in spatial search
- Renormalization of the Unitary Evolution Equation for Coined Quantum Walks
- A new type of quantum walks based on decomposing quantum states
- Nonlinear three-state quantum walks
- Localization of space-inhomogeneous three-state quantum walks
- Decoherence in the three-state quantum walk
- Universal dynamical scaling laws in three-state quantum walks
- Temperature of the three-state quantum walk
- Transport and Localization in Quantum Walks on a Random Hierarchy of Barriers
- Two-dimensional quantum central limit theorem by quantum walks
- Spectral analysis of three-state quantum walks with general coin matrices
- Three-state quantum walk on the Cayley Graph of the Dihedral Group
- Absorption Probabilities of Quantum Walks