Inter-qubit correlation dynamics driven by mutual interactions

TL;DR

This paper investigates how the correlation tensor of multi-qubit systems evolves under mutual interactions and external fields, revealing dynamics, invariants, and stabilization effects in quantum correlations.

Contribution

It provides a detailed analysis of correlation tensor dynamics in two- and three-qubit systems under various interactions and external fields, highlighting invariants and stabilization mechanisms.

Findings

Correlation trajectories can be periodic or nonperiodic depending on system frequencies.

Certain Hamiltonian classes lead to invariant density matrix families.

Strong external fields can stabilize specific correlation properties.

Abstract

A particularly useful tool for characterizing multi-qubit systems is the correlation tensor, providing an experimentally friendly and theoretically concise representation of quantum states. In this work, we analyze the evolution of the correlation tensor elements of quantum systems composed of $\frac12$-spins, generated by mutual interactions and the influence of the external field. We focus on two-body interactions in the form of anisotropic Heisenberg as well as antisymmetric exchange interaction models. The evolution of the system is visualized in the form of a trajectory in a suitable correlation space, which, depending on the system's frequencies, exhibits periodic or nonperiodic behavior. In the case of two $\frac12$-spins we study the stationary correlations for several classes of Hamiltonians, which allows a full characterization of the families of density matrices invariant under the evolution generated by the Hamiltonians. We discuss some common properties shared by the 2- and 3-qubit systems and show how a strong external field can play a stabilizing factor with respect to certain correlation characteristics.