Year: 2018
Type: article
Abstract: A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is such that its spectrum is exactly solvable with eigenangles for odd parity lattices being equally spaced, a feature that is remarkably independent of the coin. The eigenvectors are naturally specified in terms using the q -Pochhammer symbol, but can also be written in terms of elementary functions, and their entanglement can be analytically found. While the phase-space walker shares many features in common with the well-studied case of a coined walker in discrete time and space, such as ballistic growth of the walker position, it also presents novel features such as exact periodicity, and formation of cat-states in phase space. The participation ratio (PR), a measure of delocalization in walker space, is studied in the context of both kinds of quantum walks; while the classical PR increases as there is a time interval during which the quantum walks display a power-law growth ∼ t 0.825 . Studying the evolution of coherent states in phase space under the walk enables us to identify an Ehrenfest time after which the coin-walker entanglement saturates.
Authors: Sivaprasad Omanakuttan, Arul Lakshminarayan
Institution: Indian Institute of Technology Madras
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2802303484