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Hierarchy of quantum correlations in qubit-qutrit axially symmetric states

Venkat Abhignan, R. Muthuganesan

TL;DR

This paper analyzes quantum correlations in a hybrid qubit–qutrit system with axial and planar anisotropies, DM coupling, and external fields by comparing Negativity (entanglement), MIN, UIN, and Bell nonlocality under thermal noise. The authors derive the analytic thermal state for the axially symmetric Hamiltonian and formulate closed expressions for the four measures, including a qubit–qudit CHSH optimization to assess Bell nonlocality. They uncover a robust fragility hierarchy: Bell nonlocality < Negativity < MIN/UIN, with MIN and UIN persisting in parameter regions where entanglement vanishes and Bell nonlocality is absent, highlighting the practical relevance of discord-like quantities in thermally active spin systems. The results imply that, for realistic quantum information tasks in anisotropic qubit–qutrit materials, discord-type resources may be more viable than entanglement or Bell nonlocality, guiding future experimental and theoretical work toward robust quantum correlations.

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 < Negativity < 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.

Hierarchy of quantum correlations in qubit-qutrit axially symmetric states

TL;DR

This paper analyzes quantum correlations in a hybrid qubit–qutrit system with axial and planar anisotropies, DM coupling, and external fields by comparing Negativity (entanglement), MIN, UIN, and Bell nonlocality under thermal noise. The authors derive the analytic thermal state for the axially symmetric Hamiltonian and formulate closed expressions for the four measures, including a qubit–qudit CHSH optimization to assess Bell nonlocality. They uncover a robust fragility hierarchy: Bell nonlocality < Negativity < MIN/UIN, with MIN and UIN persisting in parameter regions where entanglement vanishes and Bell nonlocality is absent, highlighting the practical relevance of discord-like quantities in thermally active spin systems. The results imply that, for realistic quantum information tasks in anisotropic qubit–qutrit materials, discord-type resources may be more viable than entanglement or Bell nonlocality, guiding future experimental and theoretical work toward robust quantum correlations.

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 < Negativity < 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.
Paper Structure (9 sections, 28 equations, 6 figures)

This paper contains 9 sections, 28 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The Model and Thermalization
  3. Quantum Correlation measures
  4. Negativity
  5. Measurement-Induced Nonlocality
  6. Uncertainty-Induced Nonlocality
  7. Bell Nonlocality
  8. Results and Discussions
  9. Conclusions and outlook

Figures (6)

  • Figure 1: Thermal quantum correlations for $B_1 = 0.3, B_2 = -0.7, J = 0, K = 0.2, K_1 = -0.1, K_2 = 0.22, Dz = 0.32, \Gamma = -0.87, \Lambda = 0.31.$ Panels show: (a) Negativity, (b) Measurement-Induced Nonlocality (MIN), (c) Uncertainty-Induced Nonlocality (UIN), and (d) Bell (CHSH) parameter.
  • Figure 2: Thermal quantum correlations for $B_1 = 0.3, B_2 = -0.7, J_z = 1, K = 0.2, K_1 = -0.1, K_2 = 0.22, Dz = 0.32, \Gamma = -0.87, \Lambda = 0.31.$ Panels show: (a) Negativity, (b) Measurement-Induced Nonlocality (MIN), (c) Uncertainty-Induced Nonlocality (UIN), and (d) Bell (CHSH) parameter.
  • Figure 3: Variation of Negativity, MIN, UIN, and Bell nonlocality (CHSH parameter) as a function of the external magnetic field $B_1$. The fixed parameters are $B_2 = 0, J = -2.5, J_z = -1, K = 0.2, K_1 = -0.1, K_2 = 0.22, Dz = 0.32, \Gamma = -0.87, \Lambda = 0.31.$ Panels show: (a) Negativity, (b) Measurement-Induced Nonlocality (MIN), (c) Uncertainty-Induced Nonlocality (UIN), and (d) Bell (CHSH) parameter.
  • Figure 4: Thermal quantum correlations for $B_1 = 0, J = -2.5, J_z = -1, K = 0.2, K_1 = -0.1, K_2 = 0.22, Dz = 0.32, \Gamma = -0.87, \Lambda = 0.31.$ Panels show: (a) Negativity, (b) Measurement-Induced Nonlocality (MIN), (c) Uncertainty-Induced Nonlocality (UIN), and (d) Bell (CHSH) parameter.
  • Figure 5: Thermal quantum correlations for $B_1 = 0.3, B_2 = -0.7, J = -1.4, J_z = 1, K = 0.2, K_2 = 0.22, Dz = 0.32, \Gamma = -0.87, \Lambda = 0.31.$ Panels show: (a) Negativity, (b) Measurement-Induced Nonlocality (MIN), (c) Uncertainty-Induced Nonlocality (UIN), and (d) Bell (CHSH) parameter.
  • ...and 1 more figures