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PubblicazioneEntanglement and Quantum Complexity in Monitored Quantum Many-Body Systems(SISSA, 2025-09-15)Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
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PubblicazioneHigher-form entanglement asymmetry. Part I. The limits of symmetry breaking( 2026)Entanglement asymmetry is a relative entropy that faithfully diagnoses symmetry breaking in quantum states, possibly within a spatial subregion. In this work, we extend such framework to higher-form symmetries and compute entanglement asymmetry in theories with spontaneously-broken continuous zero- and higher-form symmetries. One of our central results is an entropic Coleman-Mermin-Wagner theorem, for 0- and p-form symmetries, valid also on subregions, which forbids spontaneous breaking of continuous p-form symmetries in spacetime dimensions d ⩽ p + 2. Our theorem not only qualifies symmetry breaking, it also quantifies it: spontaneous breaking triggers a nonvanishing entanglement asymmetry that grows monotonically towards the infrared, and counts the number of Goldstone fields. Along the way, we derive standalone results concerning the entanglement entropy and asymmetry of Goldstone bosons and gauge fields. In particular, we find a closed-form expression for the Rényi asymmetries of a compact scalar field on spherical subregions in three and four spacetime dimensions, and for higher-form gauge fields in higher dimensions.
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PubblicazioneA Stochastic Perturbation Approach to Nonlinear Bifurcating Problems( 2026)Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary. However, stochastic models typically require large computational resources to produce meaningful statistics. In this work, we leverage the Polynomial Chaos (PC) expansion to propose a systematic approach for bifurcation detection in parametric systems of equations. We show that the method, exploiting a perturbed version of the deterministic model, avoids repeated costly simulations across multiple parameter values and requires no prior information for initializing numerical solvers, while still providing accurate characterization of the bifurcation branches. We argue that the PC solutions of the perturbed model not only provide access to statistical information about the deterministic branches, but also approximate simultaneously their behavior in a single solver call. Finally, we validate our claims by means of numerical tests on the pitchfork bifurcation, examining both its normal form and a classical realization in fluid-dynamics PDEs, namely the Coandă effect.
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PubblicazioneSearching for gravitational waves with Gaia and its cross-correlation with PTA: Absolute vs differential astrometry( 2026)Astrometric missions like Gaia provide exceptionally precise measurements of stellar positions, parallaxes, and proper motions. Gravitational waves traveling between the observer and distant stars can induce small, correlated shifts in their apparent positions, a phenomenon known as astrometric deflection. The precision and scale of astrometric datasets make them well suited for searching for a stochastic gravitational-wave background, whose signature appears in the two-point correlation function of the deflection field across the sky. In space-based astrometry, the ultimate sensitivity of such measurements is reduced by systematic uncertainties in the satellite's absolute attitude reconstruction, which constrain the accuracy of absolute astrometry. These orientation errors can be mitigated by focusing on relative angular separation between pairs of stars, which effectively cancel out common-mode orientation noise. In this work, we compute the astrometric response and the overlap reduction functions for this differential approach, correcting previous expressions presented in the literature. We use a Fisher matrix analysis to compare the sensitivity of differential astrometry to that of conventional absolute astrometry. Our analysis shows that while the differential method is theoretically sound, its sensitivity is limited for closely spaced star pairs. Pairs with large angular separations provide competitive sensitivity, but, when considered in connection with Gaia, it is unclear whether the differential strategy would be effective, since instrumental systematics are not expected to remain correlated on such scales. Finally, we demonstrate that combining astrometric data with observations from pulsar-timing arrays leads to slight improvements in sensitivity at frequencies greater than or similar to 10-7Hz.
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PubblicazioneEntanglement Asymmetry in Conformal Field Theory and Holography( 2025)Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited “coherent states” in conformal quantum field theories with a U(1) symmetry, employing Euclidean path-integral methods with topological symmetry defects and the replica formalism. We compute, at leading order in perturbation theory, the asymmetry for a variety of subsystems, including finite spherical subregions in flat space, in finite volume, and at positive temperature. We also study its Lorentzian time evolution, showcasing the dynamical restoration of the symmetry due to thermalization, as well as the presence of a quantum Mpemba effect. Our results are universal, and apply in any number of dimensions. We also show that the perturbative entanglement asymmetry is related to the Fisher information metric, which has a known holographic dual called the Hollands–Wald canonical energy, and that it is captured by the anti-de-Sitter bulk charge contained in the entanglement wedge.