Molecular nanomagnets are compounds characterized by a high-spin magnetic core that is protected by organic ligands. They have recently gained attention as potential quantum information carriers in solid-state quantum computing platforms, simultaneously exhibiting classical macroscopic properties and quantum features in light of their complex nature and configuration. Addressing the condition when they manifest unquestionable quantum behavior is key to guarantee their effectiveness as resources for quantum information processing. We address the quantumness of molecular nanomagnets using a recently formulated criterion [cf. Krisnanda et al., Phys. Rev. Lett. 119, 120402 (2017)] demonstrating that these systems exhibit an intrinsic quantum nature, as evidenced by their ability to generate and enhance quantum correlations between two non-interacting probes. Our analysis, which is performed addressing various dynamical regimes, paves the way to the design of experimentally viable tests of non-classicality in multipartite registers consisting of ensembles of molecular nanomagnets.

Standard quantum metrology relies on ensemble-averaged quantities, such as the Quantum Fisher Information (QFI), which often mask the fluctuations inherent to single-shot realizations. In this work, we bridge the gap between quantum information geometry and stochastic thermodynamics by introducing the Conditional Quantum Fisher Information (CQFI). Defined via the Symmetric Logarithmic Derivative, the CQFI generalizes the classical stochastic Fisher information to the quantum domain. We demonstrate that the CQFI admits a decomposition into incoherent (population) and coherent (basis rotation) contributions, augmented by a transient interference cross-term absent at the ensemble level. Crucially, we show that this cross-term can be negative, signaling destructive interference between classical and quantum information channels along individual trajectories. Leveraging this framework, we construct a stochastic information geometry that defines thermodynamic length and action for single quantum trajectories. Finally, we derive fundamental quantum speed limits valid at the single-trajectory level and validate our results using the quantum jump unraveling of a driven thermal qubit.

Accurately estimating properties of quantum states, such as entanglement, while essential for the development of quantum technologies, remains a challenging task. Standard approaches to property estimation rely on detailed modeling of the measurement apparatus and a priori assumptions on their working principles. Even small deviations can greatly affect reconstruction accuracy and prediction reliability. Here, we demonstrate that quantum reservoir computing embodies a powerful alternative for witnessing quantum entanglement and, more generally, estimating quantum features from experimental data. We leverage the orbital angular momentum of photon pairs as an ancillary degree of freedom to enable informationally complete single-setting measurements of their polarization. Our approach does not require fine-tuning or refined knowledge of the setup, at the same time outperforming conventional approaches. It automatically adapts to noise and imperfections while avoiding overfitting, ensuring robust reconstruction of entanglement witnesses and paving the way to the assessment of quantum features of experimental multiparty states. A quantum reservoir uses photon OAM to witness entanglement without modeling, enabling robust, efficient, single-setting analysis.

We introduce and validate a machine learning-assisted protocol to classify time and space correlations of classical noise acting on a quantum system, using two interacting qubits as probe. We consider different classes of noise, according to their Markovianity and spatial correlations. Leveraging the sensitivity of a coherent population transfer protocol under three distinct driving conditions, the various noises are discriminated by only measuring the final transfer efficiencies. This approach reaches around 90% accuracy with a minimal experimental overhead