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.
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.
Nonclassicality Analysis and Entanglement Witnessing in Spin-1/2 NMR Systems
We investigate quantum features and non-classical nature of two-spin-1/2 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 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.
Entanglement plays a crucial role in quantum information science and many-body physics, yet quantifying it in mixed quantum many-body systems has remained a notoriously difficult problem. Here, we introduce families of quantitative entanglement witnesses, constructed from partial transpose and realignment moments, which provide rigorous bounds on entanglement monotones as well as entanglement dimensionality. Our witnesses can be efficiently measured using SWAP tests or variants of Bell measurements, thus making them directly implementable on current hardware. Leveraging our witnesses, we present several novel results on entanglement properties of mixed states, both in quantum information and many-body physics. We develop efficient algorithms to test whether mixed states with bounded entropy have low or high entanglement, which previously was only possible for pure states. We also provide an efficient algorithm to test the Schmidt rank using only two-copy measurements, and the operator Schmidt rank using four-copy measurements. Further, our witnesses robustly certify the quantum circuit depth in the presence of noise, as well as the Schmidt rank of mixed states. Finally, we show that the entanglement phase diagram of Haar random states, quantified by the partial transpose negativity, can be fully established solely by computing our witness, a result that also applies to any state 4 -design. Our witnesses can also be efficiently computed for matrix product states, thus enabling the characterization of entanglement in extensive many-body systems. Finally, we make progress on the entanglement required for quantum cryptography, establishing rigorous limits on pseudoentanglement and pseudorandom density matrices with bounded entropy. Our work opens new avenues for quantifying entanglement in large and noisy quantum systems.
Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots.
A bipartite quantum system in a mixed state can exhibit nonclassical correlations which can go beyond quantum entanglement. While quantum discord is the standard measure of quantifying such general quantum correlations, the nonclassicality can be determined by simpler means via the measurement of witness operators. We experimentally construct a positive map to witness nonclassicality of two qubits in an NMR system. The map can be decomposed in terms of measurable spin magnetizations so that a single run of an experiment on an ensemble of spins suffices to detect the nonclassicality in the state, if present. We let the state evolve in time and use the map to detect nonclassicality as a function of time. To evaluate the efficacy of the witness operator as a means to detect nonclassicality, we measure quantum discord by performing full quantum-state tomography at each time instant and obtain a fairly good match between the two methods.
In 1935, as part of a broader debate about the interpretation of quantum mechanics, Schrödinger introduced the term “verschränkung” (entanglement) to describe the way in which mutually-exclusive experimental outcomes could be woven together in a single quantum mechanical state. Ninety years later, entanglement is no longer a philosophical curiosity but a technological resource, central to the pursuit of quantum advantage sought in the entanglement of a few hundred qubits. In the context of condensed matter physics, the most celebrated example of entanglement arises in quantum spin liquids (QSL), exotic magnetic phases where, at comparable temperatures, billions of spins can be entangled. The sharpest distinctions between conventional magnetic phases, QSL, and states driven by disorder, are expected to be found in their entanglement properties. Yet exactly what these distinctions are, or how they might be used in experiments, remains poorly understood. In this thesis, we explore how material-based imperfections such as bond disorder and finite temperature affect experimentally accessible entanglement-based diagnostics in models of quantum spin liquids (QSLs). We ask: (1) Can spin liquid states be reliably distinguished from disorder-driven phases using such diagnostics? (2) What can these experimentally accessible entanglement witnesses reveal about the microscopic structure of entanglement in QSLs? In particular, we examine the robustness of these quantum correlations under realistic conditions where thermal fluctuations are unavoidable. In addressing (1), we find that measures like concurrence become unreliable in disordered systems. In contrast, the finite temperature scaling of multipartite diagnostics such as the quantum Fisher information (QFI) provides a more effective means of distinguishing QSLs from competing disorder-dominated phases. For (2), we investigate how the finite temperature behavior of multipartite entanglement measures obtained from semidefinite programming (SDP) methods supports a two step picture for how a high temperature paramagnet crosses over into a QSL ground state. In particular, these results provide a conceptual framework that places quantitative bounds on the temperature window over which candidate materials can be expected to exhibit the characteristic physics of the QSL ground state.