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arXiv:2512.01060 · Physical Chemistry Chemical Physics

Quantum Entanglement Control in Two-Spin-1/2 NMR Systems Through Magnetic Fields and Temperature

Fatemeh Khashami, Stefan Glöggler

quant-phSubmitted Nov 30, 2025• Announced Dec 2, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

Journal reference
Phys. Chem. Chem. Phys., 2025,27, 16996-17007
DOI
10.1039/D5CP02597D
Comments
12 pages, 6 figures

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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.
Nonclassicality Analysis and Entanglement Witnessing in Spin-1/21/21/2 NMR Systems
We investigate quantum features and non-classical nature of two-spin-1/21/21/2 NMR systems at thermal equilibrium under external magnetic fields. More specifically, using suitable quantifiers, we analyze quantum coherence, mixedness, and entanglement in NMR systems and examine their features within the system. We derive closed-form analytical expressions for the quantum elements and show how they depend on temperature and magnetic field strength. We demonstrate that at zero temperature, the system exhibits a quantum critical point, characterized by non-analytic behavior in the measures of coherence, and a sharp peak in mixedness. Moreover, we analyze the entanglement of the system using a suitable entanglement witness. This provides an experimentally friendly setting for testing entanglement in NMR systems. In other words, the witness links the entanglement in the system to quantum observables, making it directly provable in NMR experiments. We establish a connection between quantum information quantifiers and experimentally accessible NMR spectra of the system, enabling the quantification of entanglement, coherence, and mixedness through NMR signal processing.
We investigate quantum-state properties of thermal two-spin-1/2 NMR systems under external magnetic fields, with the goal of translating density-matrix-based quantum quantities into experimentally accessible NMR observables. In particular, we consider mixedness and witness-based entanglement as complementary probes of the thermal spin-state structure. Mixedness quantifies the departure of the NMR ensemble from a pure-state dominated regime and identifies field-dependent population redistribution, while the entanglement witness provides a practical test of nonclassical spin-spin entanglement without requiring full density-matrix reconstruction. Our framework links quantum-information quantities to NMR spectra, polarization observables, and spin-spin correlations, enabling the characterization of mixedness and witness-based entanglement through NMR signal analysis. We further examine the effect of noise and imperfections on the measurements. We also show how repeating the measurement improves the stability of the extracted signatures. These results provide insights for quantum-enhanced NMR, low-temperature spectroscopy, and emerging quantum sensing technologies where experimentally accessible signatures of mixedness and entanglement are needed.
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In this article, we investigate thermal entanglements of the two-site, three-site and four-site mixed spin (1/2,1) XYsystems. The entanglement versus temperature and external magnetic field is discussed. It is found that the entanglements decrease monotonically as temperature increases in the presence and absence of a weak external magnetic field. For the two-site and four-site XY systems, thermal entanglements disappear at the same temperature which is called critical temperature no matter in the ferromagnetic case or antiferromagnetic. It also shows that the critical temperature is independent of external magnetic field. For the three-site system, the corresponding critical temperature is also irrelevant to external magnetic field, while the critical temperature for the ferromagnetic case is higher than that for the antiferromagnetic case. The entanglement of XY systems can develop a few stable platform in an environment of low temperature, but the entanglement vanishes when external magnetic field exceeds some critical value. In this article, we also analyze the difference in thermal entanglement between mixed-spin system and single-spin system, and find that there exists multi-level level crossing in the mixed-spin system.
We study and compare the persistence of bipartite entanglement (BE) and multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY models in an external transverse magnetic field under the effect of thermal excitations. We compare the threshold temperature at which the entanglement vanishes in both types of entanglement. We use the entanglement of formation as a measure of the BE and the geometric measure to evaluate the ME of the system. We have found that in both dimensions in the anisotropic and partially anisotropic spin systems at zero temperatures, all types of entanglement decay as the magnetic field increases but are sustained with very small magnitudes at high field values. Also we found that for the same systems, the threshold temperatures of the nearest neighbour (nn) BEs are higher than both of the next-to-nearest neighbour BEs and MEs and the three of them increase monotonically with the magnetic field strength. Thus, as the temperature increases, the ME and the far parts BE of the system become more fragile to thermal excitations compared to the nn BE. For the isotropic system, all types of entanglement and threshold temperatures vanish at the same exact small value of the magnetic field. We emphasise the major role played by both the properties of the ground state of the system and the energy gap in controlling the characteristics of the entanglement and threshold temperatures. In addition, we have shown how an inserted magnetic impurity can be used to preserve all types of entanglement and enhance their threshold temperatures. Furthermore, we found that the quantum effects in the spin systems can be maintained at high temperatures, as the different types of entanglements in the spin lattices are sustained at high temperatures by applying sufficiently high magnetic fields.
Non-classical correlations arise in various quantum mechanical systems. Characterization and quantification of these correlations is an important and active branch of research in the field of quantum information theory. Investigation of non-classical correlations in condensed matter systems gives important insights about the characteristics of these systems. In particular, systems possessing a quantum critical point in their phase diagrams have attracted much attention due to the peculiar behavior of correlations near these points. In this thesis, we have investigated two distinct quantum spin models from the perspective of correlations and, we have discussed the correlation content of an important subclass of bipartite states. We start by an analytical calculation of the quantum discord for a system composed of spin-j and spin-1/2 subsystems possessing rotational symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in rotationally invariant states the amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have compared their quantum discord with entanglement and seen that quantum discord is higher than the entanglement. Next, we have investigated the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. We have demonstrated that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement. Finally, we have investigated various thermal quantum and total correlations in the anisotropic XY spin-chain with transverse magnetic field. We have shown that the ability of the considered measures to estimate the critical points of this system at finite temperature strongly depends on the anisotropy parameter of the Hamiltonian. Furthermore, we have studied the effect of temperature on long-range correlations of the XY chain.