Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain

TL;DR

This paper investigates how a qubit's dynamics are influenced by a spin environment, revealing a tunable transition between Markovian and non-Markovian behavior, with implications for quantum information processing.

Contribution

It identifies a specific parameter point where qubit dynamics switch from Markovian to non-Markovian, and characterizes the qubit channel using quantum process tomography.

Findings

Existence of a parameter point with Markovian dynamics

Ability to tune between forgetful and strongly affected regimes

Complete characterization of the qubit channel

Abstract

Using recently proposed measures for non-Markovianity [H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. {\bf 103}, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We show the existence of a point, in the parameter space of the system, where the qubit dynamics is effectively Markovian and that such a point separates two regions with completely different dynamical behaviors. Indeed, our study demonstrates that the qubit evolution can in principle be tuned from a perfectly forgetful one to a deep non-Markovian regime where the qubit is strongly affected by the dynamical back-action of the environmental spins. By means of quantum process tomography, we provide a complete and intuitive characterization of the qubit channel.