We investigate the entanglement properties in the symmetric subspace of N-partite d-dimensional systems (qudits). As it happens already for bipartite diagonal symmetric states, also in the multipartite case the local dimension d plays a crucial role. Here, we demonstrate that there is no bound entanglement for d = 3, 4 and N = 3. Using different techniques, we present strong analytical evidence that no bound entanglement exist for any N if d ≤ 4. Interestingly, bound entanglement of diagonal symmetric states exist for any number of parties, N ≥ 2, and local dimensions d ≥ 5.

We investigate the entropy production in the Diósi-Penrose (DP) model, one of the most extensively studied gravity-related collapse mechanisms, and one of its dissipative extensions. To this end, we analyze the behavior of a single harmonic oscillator, subjected to such collapse mechanisms, focusing on its phase-space dynamics and the time evolution of the entropy production rate, a central quantity in non-equilibrium thermodynamics. Our findings reveal that the original DP model induces unbounded heating, producing dynamics consistent with the Second Law of thermodynamics only under the assumption of an infinite-temperature noise field. In contrast, its dissipative extension achieves physically consistent thermalization in the regime of low dissipation strength. We further our study to address the complete dynamics of the dissipative extension, thus including explicitly non-Gaussian features in the state of the system that lack from the low-dissipation regime, using a short-time approach.

The estimation of properties of quantum states – such as entanglement – is a core need for the development of quantum technologies, yet remaining a demanding challenge. Standard approaches to property estimation rely on the modeling of the measurement apparatus and, often, a priori assumptions on their working principles. Even small deviations can greatly affect reconstruction accuracy and prediction reliability. Machine learning (ML) techniques have been proven promising to overcome these difficulties. However, interpretability issues related to overfitting limit the usefulness of existing ML methods when high precision is requested. Here, we demonstrate that quantum extreme learning machines (QELMs) embody a powerful alternative for witnessing quantum entanglement and, more generally, for estimating features of experimental quantum states. We implement a photonic QELM that leverages the orbital angular momentum of photon pairs as an ancillary degree of freedom to enable informationally complete single-setting measurements of the entanglement shared by their polarization degrees of freedom. Unlike conventional methods, our approach does not require fine-tuning, precise calibration, or refined knowledge of the apparatus. In contrast, it automatically adapts to noise and imprecisions while avoiding overfitting, thus ensuring the robust reconstruction of entanglement witnesses and paving the way to the assessment of quantum features of experimental multi-party states.

Spectral densities encode essential information about system-environment interactions in open-quantum systems, playing a pivotal role in shaping the system’s dynamics. In this work, we leverage machine learning techniques to reconstruct key environmental features, going beyond the weak-coupling regime by simulating the system’s dynamics using the reaction coordinate mapping. For a dissipative spin-boson model with a structured spectral density expressed as a sum of Lorentzian peaks, we demonstrate that the time evolution of a system observable can be used by a neural network to classify the spectral density as comprising one, two, or three Lorentzian peaks and accurately predict their central frequency.