Limit distributions of three-state quantum walks: the role of coin eigenstates
arXiv:1405.7146 · doi:10.1103/PhysRevA.90.012342
Abstract
We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the description of the walk simplifies considerably when the initial coin state is decomposed in the basis formed by the eigenvectors of the coin operator. This allows us to express the limit distributions in a much more convenient form. Consequently, striking features which are hidden in the standard basis description are easily identified. Moreover, the dependence of moments of the position distribution on the initial coin state can be analyzed in full detail. In particular, we find that in the eigenvector basis the even moments and the localization probability at the origin depend only on incoherent combination of probabilities. In contrast, odd moments and localization outside the origin are affected by the coherence of the initial coin state.
References in corpus (8)
- Universal computation by quantum walk
- Quantum walks of correlated particles
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Discrete single-photon quantum walks with tunable decoherence
- Limit distributions of two-dimensional quantum walks
- Weak Limit of the 3-State Quantum Walk on the Line
- Continuous deformations of the Grover walk preserving localization
Cited by in corpus (12)
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- Lackadaisical quantum walks on 2D grids with multiple marked vertices
- Localization of space-inhomogeneous three-state quantum walks
- Nonlinear three-state quantum walks
- Universal dynamical scaling laws in three-state quantum walks
- Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
- Lackadaisical quantum walks on triangular and honeycomb 2D grids
- Three-state quantum walk on the Cayley Graph of the Dihedral Group
- Spectral analysis of three-state quantum walks with general coin matrices