Hierarchy of quantum correlations in qubit-qutrit axially symmetric states

TL;DR

This paper explores the robustness of various quantum correlations in a qubit-qutrit system under anisotropic conditions, revealing that discord-like measures are more resilient than entanglement and Bell nonlocality in thermal environments.

Contribution

It introduces a comprehensive analysis of quantum correlations in a hybrid qubit-qutrit system, including a tailored Bell nonlocality measure for asymmetric states, and establishes a hierarchy of their fragility.

Findings

Bell nonlocality is the most fragile quantum correlation under thermal noise.

Negativity and other discord-like measures are more robust and persist where entanglement vanishes.

The study confirms a fragility hierarchy: Bell nonlocality ⊂ Negativity ⊂ UIN(MIN).

Abstract

We investigate quantum correlations in a hybrid qubit-qutrit system subject to both axial and planar single-ion anisotropies, dipolar spin-spin interactions, and Dzyaloshinskii-Moriya (DM) coupling. Using Negativity, Measurement-Induced Non-locality (MIN), Uncertainty-Induced Nonlocality (UIN), and Bell nonlocality (as quantified by the CHSH inequality) as measures, we analyze the interplay between anisotropy parameters, magnetic fields, and temperature on the survival of quantum correlations. Our results demonstrate that Bell nonlocality and entanglement (Negativity) are highly sensitive to temperature and anisotropy, exhibiting sudden death under thermal noise, whereas MIN and UIN are significantly more robust. In particular, these discord-like and information-theoretic measures provide the largest baseline and persist even in parameter regions where entanglement vanishes, highlighting their suitability as a quantumness witness in realistic conditions. Notably, our Bell nonlocality study is tailored to the asymmetric qubit-qutrit setting by exploiting a recently developed qubit-qudit CHSH maximization framework. However, Bell nonlocality is confirmed to be the most fragile, surviving only in narrow parameter windows at low temperature. A key finding of this work is that we observe the fragility hierarchy: Bell nonlocality $\subseteq$ Negativity $\subseteq$ UIN(MIN) in the qubit-qutrit setting. These results provide deeper insight into the relative robustness of distinct quantum resources in anisotropic qubit-qutrit models, suggesting that quantum discord-like measures, such as MIN and UIN, may serve as more practical resources than entanglement for quantum information tasks in thermally active spin systems.