We investigate the behaviors of thermal entanglement, quantum correlation beyond entanglement namely, measurement-induced nonlocality (MIN) and coherence in a nickel radical molecular magnet (Et3NH)[Ni(hfac)2L], whose spin-spin interactions are well described by the Heisenberg model. Using experimentally estimated coupling parameters, we compute the thermal state of the system and analyze the dependence of quantum resources on temperature and magnetic field. The results indicate that the quantum resources of the nickel-radical molecular magnet persist even at room temperature. We show that while negativity (the entanglement measure) rapidly vanishes with increasing temperature and magnetic field, measurement-induced nonlocality and quantum coherence remain comparatively more stable and persist in regions where entanglement is absent. These results highlight the significance of nonclassical correlations beyond entanglement in thermally activated spin systems and suggest that such molecular magnets could serve as viable platforms for quantum information processing in realistic conditions.
Journal reference
Journal of Magnetism and Magnetic Materials 645 (2026) 173981
We investigate the behaviors of thermal entanglement, quantum correlation beyond entanglement namely, measurement-induced nonlocality (MIN) and coherence in a nickel radical molecular magnet (Et3NH)[Ni(hfac)2L], whose spin-spin interactions are well described by the Heisenberg model. Using experimentally estimated coupling parameters, we compute the thermal state of the system and analyze the dependence of quantum resources on temperature and magnetic field. The results indicate that the quantum resources of the nickel-radical molecular magnet persist even at room temperature. We show that while negativity (the entanglement measure) rapidly vanishes with increasing temperature and magnetic field, measurement-induced nonlocality and quantum coherence remain comparatively more stable and persist in regions where entanglement is absent. These results highlight the significance of nonclassical correlations beyond entanglement in thermally activated spin systems and suggest that such molecular magnets could serve as viable platforms for quantum information processing in realistic conditions.
Bipartite entanglement is comprehensively investigated in the mononuclear molecular complex (Et3NH)[Ni(hfac)2L], where HL denotes 2-(2-hydroxy-3-methoxy-5-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-3-oxide-1-oxyl and hfacH stands for hexafluoroacetylacetone. From the magnetic point of view, the molecular compound (Et3NH)[Ni(hfac)2L] consists of an exchange-coupled spin-1 Ni2+ magnetic ion and a spin-12 nitronyl-nitroxide radical substituted nitrophenol. The nickel-radical molecular complex affords an experimental realization of a mixed spin-(12, 1) Heisenberg dimer with a strong antiferromagnetic exchange coupling, J/kB = 505 K, and two distinct g-factors, gRad = 2.005 and gNi = 2.275. By adopting this set of magnetic parameters, we demonstrate that the Zeeman splitting of a quantum ferrimagnetic ground-state doublet due to a weak magnetic field may substantially reinforce the strength of bipartite entanglement at low temperatures. The molecular compound (Et3NH)[Ni(hfac)2L] maintains sufficiently strong thermal entanglement, even at room temperature, vanishing only above 546 K. Specifically, the thermal entanglement in the nickel-radical molecular complex retains approximately 40% of the maximum value, corresponding to perfectly entangled Bell states at room temperature, which implies that this magnetic compound provides a suitable platform of a molecular qubit with potential implications for room-temperature quantum computation and quantum information processing.
Quantum correlations and coherence in a two-qubit anisotropic XY under magnetic field
We study thermal quantum correlations and coherence in Heisenberg XY model with anisotropic interactions under a uniform magnetic field $ B $. Using concurrence C, local quantum uncertainty (LQU), Bell-Clauser-Horne-Shimony-Holt (CHSH) nonlocality $ \mathbb{B}$, and coherence Cl as quantifiers, we analyze how magnetic anisotropy $ δ_m $, coupling anisotropy $ δ_c $, Dzyaloshinskii-Moriya (DM) interaction $ D $, temperature $ T $, and magnetic field $ B $ modulate quantum resources. At low temperatures and relevant magnetic fields, the entanglement is maximized, but exhibits sudden death for $ δ_m = 0 $, which turns into a smooth decay as $ δ_m $ increases, highlighting its stabilizing role. LQU shows that stronger anisotropy suppresses quantum correlations, while $ \mathbb{B} $ induces a non-monotonic response peaking at a critical field $ B_c .Bell−CHSHnonlocalityviolations( \mathbb{B} > 2 $) persist below $ B_c ,butthermalnoise( T \geq 1 $) suppresses them. Coherence $ C_l $ is most robust to thermal fluctuations, especially for high δm, which also dampens abrupt quantum phase transitions. The DM interaction is essential for entanglement generation, with $ D $ and anisotropy synergistically enhancing correlation resilience. We identify a hierarchy of thermal degradation: nonlocality ($ \mathbb{B} )vanishesfirst,followedbyentanglement( C $), then general quantum correlations (LQU), while coherence $ C_l $ persists the longest. These results demonstrate tunable control of quantum resources via anisotropy and external parameters, providing insights for the design of robust spin-based quantum technologies.
The bipartite entanglement in pure and mixed states of a quantum spin-1 Heisenberg dimer with exchange and uniaxial single-ion anisotropies is quantified through the negativity in a presence of the external magnetic field. At zero temperature the negativity shows a marked stepwise dependence on a magnetic field with two abrupt jumps and plateaus, which can be attributed to the quantum antiferromagnetic and quantum ferrimagnetic ground states. The magnetic-field-driven phase transition between the quantum antiferromagnetic and quantum ferrimagnetic ground states manifests itself at nonzero temperatures by a local minimum of the negativity, which is followed by a peculiar field-induced rise of the negativity observable in a range of moderately strong magnetic fields. The rising temperature generally smears out abrupt jumps and plateaus of the negativity, which cannot be distinguished in the relevant dependencies above a certain temperature. It is shown that the thermal entanglement is most persistent against rising temperature at the magnetic field, for which an energy gap between a ground state and a first excited state is highest. Besides, temperature variations of the negativity of the spin-1 Heisenberg dimer with an easy-axis single-ion anisotropy may exhibit a singular point-kink, at which the negativity has discontinuity in its first derivative. The homodinuclear nickel complex [Ni2(Medpt)2(μ-ox)(H2O)2](ClO4)2·2H2O provides a suitable experimental platform of the antiferromagnetic spin-1 Heisenberg dimer, which allowed us to estimate a strength of the bipartite entanglement between two exchange-coupled Ni2+ magnetic ions on the grounds of the interaction constants reported previously from the fitting procedure of the magnetization data. It is verified that the negativity of this dinuclear compound is highly magnetic-field-orientation dependent due to presence of a relatively strong uniaxial single-ion anisotropy.
We investigate key quantum characteristics of the mixed spin-(1/2,1,1/2) Heisenberg trimer under the influence of an external magnetic field. Specifically, we analyze the distributions of bipartite and tripartite entanglement quantified through the respective negativities and the l1-norm of coherence with the help of rigorous analytical and numerical methods. Our findings suggest that the heterotrinuclear molecular nanomagnet $[{{{\text{Cu}}^{2+}\text{L}}}_{2}{\text{Ni}}^{2+}{({\text{H}}_{2}\text{O})}_{2}]{({\text{ClO}}_{4})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}3{\text{H}}_{2}\text{O}$, which represents an experimental realization of the mixed spin-(1/2,1,1/2) Heisenberg trimer, exhibits a significant bipartite entanglement between Cu2+ and Ni2+ magnetic ions along with robust tripartite entanglement among all three constituent Cu2+Ni2+Cu2+ magnetic ions. The significant bipartite and tripartite entanglement persists even at relatively high temperatures up to 37K and magnetic fields up to 46T, whereby the coherence is maintained even at elevated temperatures. It is evidenced that the aforementioned molecular complex with the magnetic core Cu2+Ni2+Cu2+ provides an intriguing quantum resource, which exhibits a star-shaped state within the singlet eigenstate at low magnetic fields and W-like state within the triplet eigenstate at moderate magnetic fields.
We investigate quantum entanglement in two-spin-1/2 NMR systems at thermal equilibrium under external magnetic fields. We derive closed-form analytical expressions for the entanglement of the system and show how the entanglement depends on temperature and magnetic field strength, resulting in a threshold temperature beyond which entanglement vanishes. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measure of entanglement. We further develop analytical criterion for level crossing, which serves as a condition for identifying quantum critical points in both homonuclear and heteronuclear systems, and apply it to multiple settings to analyze their quantum critical points. We establish a direct link between the quantum entanglement quantifier and experimentally accessible NMR observables, enabling entanglement to be quantified through NMR signal processing. This provides a practical framework for characterizing quantum correlations using standard NMR experiments. These findings provide insights into the thermal control of quantum features, with implications for quantum-enhanced NMR, low-temperature spectroscopy, and emerging quantum technologies.
Abstract This research investigates the dynamics of entanglement and uncertainty‐induced nonlocality (UIN) in a spin‐1/2 Ising‐Heisenberg diamond chain subjected to local non‐Markovian decoherence channels. By examining amplitude damping (AD) and random telegraph noise (RTN) in both zero and finite temperature regimes, the study reveals nuanced distinctions in the degradation and revival of quantum correlations. The interplay between intrinsic spin couplings, thermal effects, and memory‐induced coherence backflow highlights the complex behavior of quantum resources under realistic noise conditions. Concurrence emerges as a sensitive marker of entanglement recovery in dephasing environments, while uncertainty‐induced nonlocality proves more resilient in high‐temperature or dissipative regimes. The analysis further demonstrates that moderate thermal activation and external magnetic fields can nontrivially enhance or suppress quantum features depending on system parameters. These findings offer a detailed perspective on the robustness and complementarity of different quantum correlation measures, providing guiding principles for the design of thermally stable and noise‐resilient quantum information protocols.