Aspects of quantum states asymmetry for the magnetic dipolar interaction dynamics

TL;DR

This paper explores the asymmetry properties of quantum states under magnetic dipolar interaction, analyzing their relation to entanglement and proposing measures to quantify asymmetry in different scenarios.

Contribution

It introduces and compares new asymmetry measures based on Wigner-Yanase skew information and group elements for states evolving under MDI Hamiltonian.

Findings

Asymmetry depends on Hamiltonian parameters and initial states.

Local state asymmetry dynamics are characterized over time.

Group generator-based measure is inadequate due to null eigenvalue issue.

Abstract

We investigate the asymmetry properties of quantum states in relation to the Hamiltonian responsible for the magnetic dipolar interaction (MDI) dynamics, and we evaluate its relationship to entanglement production. We consider some classes of pure and mixed quantum states of two qubits evolved under MDI and, using the asymmetry measure defined via the Wigner-Yanase skew information, we describe the asymmetry dependence on the Hamiltonian parameters and initial conditions of the system. In addition, we define and calculate the dynamics of the asymmetry of local states, characterizing their temporal and interaction parameters dependence. Finally, because the MDI Hamiltonian has a null eigenvalue, the group generator-based asymmetry measure does not adequately quantify the state susceptibility with respect to the action of the subspace generated by the eigenvectors associated with this eigenvalue. For this reason, we also define and study the group element-based asymmetry measure with relation to the unitary operator associated with the MDI Hamiltonian.