Extracting meaningful information about unknown quantum states without performing a full tomography is an important task. Low-dimensional projections and random measurements can provide such insight but typically require careful crafting. In this paper, we present an optical scheme based on sending unknown input states through a multimode fiber and performing two-point intensity and coincidence measurements. A short multimode fiber implements effectively a random projection in the spatial domain, while a long-dispersive multimode fiber performs a spatial and spectral projection. We experimentally show that useful properties, i.e., the purity, dimensionality, and degree of indistinguishability of various states of light including spectrally entangled biphoton states, can be obtained by measuring statistical properties of single counts and their correlation between two outputs over many realizations of unknown random projections. Moreover, we show that this information can then be used for state classification.

The characterisation of quantum networks is fundamental to understanding how energy and information propagates through complex systems, with applications in control, communication, error mitigation and energy transfer. In this work, we explore the use of external probes to infer the network topology in the context of continuous-time quantum walks, where a single excitation traverses the network with a pattern strongly influenced by its topology. The probes act as decay channels for the excitation, and can be interpreted as performing an indirect measurement on the network dynamics. By making use of a Genetic Optimisation algorithm, we demonstrate that the data collected by the probes can be used to successfully reconstruct the topology of any quantum network with high success rates, where performance is limited only by computational resources for large network sizes. Moreover, we show that increasing the number of probes significantly simplifies the reconstruction task, revealing a tradeoff between the number of probes and the required computational power.

We realize fast thermalization and state preparation of a single mode cavity field using a collision model-like approach, where a sequence of qubits or three level system ancillae, sequentially interacting with the field, is engineered with a genetic algorithm approach. In contrast to optimal control techniques, there is no time-dependent system Hamiltonian control deployed and, in contrast to reservoir engineering, the engineered full system-environment dynamics is optimized, and the target is not a steady state. We prove a significant speed up in thermalization - for which we show that diagonal qubit ancilla states are sufficient - and in the preparation of coherent states. We demonstrate the preparation of squeezed states and of highly non-Gaussian states. Our work offers a new alternative for fast preparation of cavity states that lays in between optimal Hamiltonian control and reservoir engineering, and gives further insights on the resources needed to realize or speed up the preparation of such states.

Waveguide quantum electrodynamics (QED) studies the interaction between quantum emitters and guided photons in one-dimension. When the waveguide hosts interacting photons, it becomes a platform to explore many-body quantum optics. However, the influence of photonic correlations on emitter dynamics remains poorly understood. In this work, we study the collective decay and coherent interactions of quantum emitters coupled to a one-dimensional Bose-Hubbard waveguide, an array of coupled photonic modes with repulsive on-site interactions that supports superfluid and Mott insulating phases. We show that photon-photon interactions alone can trigger a superradiant burst, independent of emitter spacing and transition frequency. In the off-resonant regime, emitters exhibit two distinct types of mediated interactions: delocalized superfluid excitations yield distance-independent couplings, while Mott-insulator quasiparticles generate short-range interactions mediated by doublons and holons. Our work bridges many-body physics and waveguide QED, revealing how photonic many-body states shape emitter dynamics.