Mixedness and entanglement witnessing analysis in two-spin-1/2 NMR systems

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.