Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
arXiv:2212.00540 · doi:10.1088/1402-4896/accf43
Abstract
Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site recurrence probability) depends on the coin parameter and the probability that the walker is initially in a particular coin state for which the walk returns to the origin with certainty. Finally, we present a brief investigation of the exact quantum state recurrence.
References in corpus (20)
- Quantum Computation and Decision Trees
- From quantum cellular automata to quantum lattice gases
- Recurrence for discrete time unitary evolutions
- Recurrence and Pólya number of quantum walks
- Recurrence properties of unbiased coined quantum walks on infinite -dimensional lattices
- Quantum recurrence of a subspace and operator-valued Schur functions
- Asymptotic dynamics of coined quantum walks on percolation graphs
- Probing Measurement Induced Effects in Quantum Walks via Recurrence
- Wigner formula of rotation matrices and quantum walks
- Limit distributions of three-state quantum walks: the role of coin eigenstates
- On a class of quantum channels, open random walks and recurrence
- Continuous deformations of the Grover walk preserving localization
- Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems
- Quantized recurrence time in iterated open quantum dynamics
- Discrete time quantum walks on percolation graphs
- Percolation induced effects in 2D coined quantum walks: analytic asymptotic solutions
- Site recurrence of open and unitary quantum walks on the line
- Quantum Markov chains: recurrence, Schur functions and splitting rules
- Suitable bases for quantum walks with Wigner coins
- Conditional limit measure of one-dimensional quantum walk with absorbing sink