Classifying the non-time-local and entangling dynamics of an open qubit system

TL;DR

This paper investigates how symmetry and coupling strength influence the dynamics of an open qubit system, revealing conditions for non-time-local behavior and the impact of environment perturbations on effective descriptions.

Contribution

It establishes the relationship between symmetry, entanglement, and non-Markovianity in open quantum systems with both time-independent and time-dependent Hamiltonians.

Findings

Symmetry affects the non-time-locality of qubit dynamics.

Perturbing the environment yields effective time-local models.

Changing symmetry in time-dependent Hamiltonians dramatically alters qubit behavior.

Abstract

We study families of dynamical maps generated from interactions with varying degrees of symmetry. For a family of time-independent Hamiltonians, we demonstrate the relationship between symmetry, strong-coupling, perfect entanglers, non-Markovian features, and non-time-locality. We show that by perturbing the initial environment state, effective time-local descriptions can be obtained that are non-singular yet capture essential non-unitary features of the reduced dynamics. We then consider a time-dependent Hamiltonian that changes the degree of symmetry by activating a dormant degree of freedom. In this example we find that the one-qubit reduced dynamics changes dramatically. These results can inform the construction of effective theories of open systems when the larger system dynamics is unknown.