Disorder and entropy rate in discrete time quantum walks

I. Vakulchyk, M. V. Fistul, Pinquan Qin +1 more

Nur Izzati Ishak, Sithi Vinayakam Muniandy, Wu Yi Chong

Bálint Kollár, Mátyás Koniorczyk

The amount of information generated by a discrete time stochastic processes in a single step can be quantified by the entropy rate. We investigate the differences between two discrete time walk models, the discrete time quantum walk and the classical random walk, in terms of entropy rate. We develop analytical methods to calculate and approximate it. This allows us to draw conclusions about the differences between classical stochastic and quantum processes in terms of the classical information theory.

Diego de Falco, Dario Tamascelli, Centro Interdipartimentale +1 more

L. A. Toikka

We observe the onset of nonergodicity from ballistic propagation of a two-body bound state in an interacting discrete-time quantum walk (DTQW) due to time-dependent disorder in the interaction. The effect of the disorder on the two-body state can be interpreted as Anderson-type localization in a projected DTQW, but without saturation of entanglement entropy. We characterize the two-body localization in terms of the rate of growth of entanglement entropy and compute the localization length. We find indications for two distinct growth laws for the entanglement: A logarithmic law in the delocalized phase and a double-logarithmic law in the localized phase. We discuss similarities with many-body localization.

Shuva Mondal, Amrita Mandal, Ujjwal Sen

We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of the quantum walker is finite, contrary to the behavior of a classical random walker, indicating an infinite resource reduction on moving over to a quantum version of a walker. Furthermore, numerical simulations indicate a reversal of this behavior due to the insertion of disorder in the walker's step lengths. Additionally, we demonstrate that in the presence of an absorber, there is a speed-up in the spreading rate, and that a disordered quantum walk that is sub-ballistic regains the ballistic spreading of a clean quantum walk.