The field of quantum information processing seeks to transform modern information technology, with applications such as quantum computing and distributed quantum networks illustrating its potential. The key ingredient underlying these applications is entanglement, a purely quantum property that allows disjoint systems to become correlated beyond classical limitations. Entanglement enables core protocols including quantum teleportation and entanglement swapping, which are well studied in few-body settings. However, extending these concepts to many-body systems is non-trivial, and forms the primary focus of this thesis. Concretely, the first half of this thesis focuses on the characterization and quantification of entanglement in generic quantum settings. These ideas culminate in the formulation of a many-body entanglement swapping protocol, describing the redistribution of entanglement between extended systems that have no prior causal connection. To test this protocol, a classical simulation of up to $20$ qubits is carried out, and the resulting entanglement is analyzed using various quantities, most notably von Neumann entropy, mutual information, and observable spin correlation functions. The simulations realize entanglement swapping between causally disconnected many-body systems, induced by measurements on auxiliary subsystems. This is captured by an increase in post-measurement mutual information and spin correlation functions when spin-conserving systems are considered. When the spin conservation requirement is relaxed, observable spin correlations become suppressed while mutual information remains largely unchanged, highlighting the regimes where observable correlation measures remain informative probes of the underlying entanglement dynamics.
The field of quantum information processing seeks to transform modern information technology, with applications such as quantum computing and distributed quantum networks illustrating its potential. The key ingredient underlying these applications is entanglement, a purely quantum property that allows disjoint systems to become correlated beyond classical limitations. Entanglement enables core protocols including quantum teleportation and entanglement swapping, which are well studied in few-body settings. However, extending these concepts to many-body systems is non-trivial, and forms the primary focus of this thesis. Concretely, the first half of this thesis focuses on the characterization and quantification of entanglement in generic quantum settings. These ideas culminate in the formulation of a many-body entanglement swapping protocol, describing the redistribution of entanglement between extended systems that have no prior causal connection. To test this protocol, a classical simulation of up to 20 qubits is carried out, and the resulting entanglement is analyzed using various quantities, most notably von Neumann entropy, mutual information, and observable spin correlation functions. The simulations realize entanglement swapping between causally disconnected many-body systems, induced by measurements on auxiliary subsystems. This is captured by an increase in post-measurement mutual information and spin correlation functions when spin-conserving systems are considered. When the spin conservation requirement is relaxed, observable spin correlations become suppressed while mutual information remains largely unchanged, highlighting the regimes where observable correlation measures remain informative probes of the underlying entanglement dynamics.
The characterization of the dynamical structure of quantum many-body systems is an important and very active endeavor both experimentally and theoretically. Several tools, such as quantum-information theoretic observables and spectral measures, provide a powerful lens for characterizing correlations and their dynamics in quantum many-body systems. These quantities can reveal important features of experimentally realizable systems and provide insight into their control and dynamical behaviour. This thesis investigates nonequilibrium settings in which the spreading and redistribution of quantum correlations exhibit unconventional behaviour, with particular emphasis on the role of extended-range correlations. We consider two main classes of systems: lattice models undergoing quantum quenches and central-spin models motivated by experimental applications. For lattice systems, we study the dynamics of entanglement and local symmetry breaking in free fermionic and bosonic models, interacting integrable systems, and quantum circuits. We first investigate symmetry restoration following quenches from ground states of long-range fermionic Hamiltonians. We show that two states undergoing symmetry restoration can exhibit multiple inversions, manifested through multiple crossings of the distance measure, implying either the evasion of the quantum Mpemba effect or a more intricate route to its occurrence. This demonstrates that anomalous relaxation is not restricted to short times and can be understood through the momentum-dependent distribution and velocities of quasiparticle excitations. We then study quenches from initial states possessing extensive, spatially organized entanglement, moving beyond the conventional setting of weakly entangled initial states. For crosscap states, characterized by antipodal correlations and volume-law entanglement entropy, we uncover unconventional entanglement dynamics and formulate an antipodal quasiparticle picture in which initially entangled degrees of freedom originate from macroscopically separated points. We subsequently generalize this construction to entangled multipodal states, whose polygon-like correlation structure produces richer equilibrium and dynamical entanglement patterns. We further investigate charge-deformed crosscap states and show that their local symmetry-breaking dynamics can display the unusual phenomenon of dynamical symmetry breaking under symmetry-preserving evolution. Finally, we extend the crosscap construction to bosonic systems and describe the dynamics of the entanglement entropy, mutual information, and logarithmic negativity within a corresponding quasiparticle framework. The second class of systems considered concerns central-spin models and their application to quantum memories in semiconductor quantum dots. We investigate how disorder in couplings and frequencies modifies collective many-body dynamics and affects the storage and retrieval of quantum information. Using spectral, dynamical, and information-theoretic diagnostics, we characterize the resulting dynamical regimes and relate the loss of collectivity and the spreading of information through the spin bath to the performance of quantum-memory protocols. Overall, the results demonstrate how extended-range correlations, whether encoded in an initial state or generated by the interaction structure, can qualitatively reshape entanglement spreading, symmetry dynamics, and information retention in nonequilibrium quantum many-body systems.
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.
One of the most important predictions of quantum mechanics is the existence of quantum entanglement. Since the inception of quantum theory, the study of entanglement has become ubiquitous in several branches of physics, from high energy to condensed matter physics and quantum information. To this avail, different measures of entanglement in quantum systems have been introduced. The most successful ones are the von Neumann and the Rényi entanglement entropies, which have been heavily studied both in lattice models and in quantum field theories (QFTs). A different, more complete characterization of entanglement is provided by the entanglement (or modular) Hamiltonian, defined as the logarithm of the reduced density matrix. One of the key property of this operator is that, under generic conditions, in 1+1-dimensional conformal field theories (CFTs) presents a local and few-body structure. Beyond just being of theoretical interest, this property has been recently used to efficiently construct the ground state of spin chains in quantum simulators. A recently introduced generalisation of the entanglement Hamiltonian is the negativity Hamiltonian, a non-Hermitian operator which is more useful for mixed states and tripartite entanglement. In this thesis we study these quantifications in many-body quantum systems and in QFTs. In the first part of the thesis, we focus on fermionic systems at equilibrium, and we obtain analytical expressions for the entanglement and the negativity Hamiltonians in the massless Dirac fermion QFT, both in presence of boundaries and at finite temperature. We compare these predictions in the continuum QFT with numerical calculations on the lattice, showing that a proper comparison requires a non-trivial continuum limit of the lattice expression, which we detail. We also investigate a lattice realisation of a non-unitary CFT, the bc-ghost theory, showing that the entanglement Hamiltonian presents an additional term with respect to the unitary case. In the second part, we study the entanglement entropies in an integrable QFT, the massless renormalisation group flow from the tricritical to the critical Ising CFT, demonstrating that the entropy is monotonically decreasing under the renormalisation group flow, as expected from the entropic c-theorem. In the third part we consider out-of-equilibrium problems. We study the melting of a domain wall configuration, computing analytically the entanglement Hamiltonian and showing that the insertion of a defect dramatically modifies the entanglement properties, changing the growth of the entropies from logarithmic to linear in time. Finally, we study generic quantum quenches in free fermionic theories, using the celebrated quasiparticle picture to obtain a prediction for the evolution of the entanglement Hamiltonian during the quench.
This thesis is devoted to the theoretical characterization and generation of strongly correlated many-body states from the perspective of quantum information theory.We first study the entanglement properties of general many-body states and define a new measure for multipartite entanglement, the "Localizable Entanglement (LE)".It quantifies the maximal entanglement that can be localized, on average, between two parties by performing local measurements on the other parties.This measure provides knowledge of the "entanglement length", which is of particular importance in the context of quantum repeaters for long-distance quantum communication.We prove upper and lower bounds on LE in terms of two-body correlation functions and develop a method for the numerical computation of LE in one-dimensional spin systems.We analyze the localizable entanglement in various spin systems and observe characteristic features for a quantum phase transition such as a diverging entanglement length.In the second part of the thesis we focus on a specific many-body system: ultra-cold atoms in an optical lattice.This system is a promising candidate for the first physical realization of a "quantum simulator", but the temperature in current experiments is still too high.We propose, analyze and compare several schemes to cool the atoms close to the ground state of the strong interaction regime.In particular, we devise an algorithmic cooling protocol that combines occupation number filtering with spin-dependent lattice shifts.In addition, we propose two different physical realizations of filtering and also design protocols that generate an ensemble of quantum registers for quantum computation.In the third part we propose how to create entanglement in small atomic clouds by deforming and rotating the harmonic trapping potential.The resulting states are entangled in their motional degrees of freedom and can be identified with strongly correlated fractional quantum Hall states.For the case of two, three and four atoms we show how to adiabatically transform the unentangled ground state into the desired entangled state.We further discuss characteristic features of these states and propose how to create and detect them experimentally using an optical lattice setup. A Proof of the lower bound on LEA.1 Theorem on connected correlation functions and local measurements . . . . . . . . .
As Schroedinger already recognised one century ago, entanglement is at the core of quantum mechanics. Nowadays it turns out to be the fundamental notion behind many quantum phenomena, from quantum algorithms to gravity, passing by critical phenomena and topological phases of matter, triggering unexpected connections between apparently far branches of physics. At the center of all these ideas, we find the (Rényi) entanglement entropies, which are powerful entanglement measures that provide fundamental insights into the investigated system or theory. This motivates the development of techniques for determining it, such as the replica trick: its implementation via the path-integral finds a wide place in this thesis. For example, we develop an efficient strategy to compute a generalised version of the Rényi entropies for all the eigenstates of a (1+1)-dimensional conformal field theory. This represents the starting point for a simulation scheme ideal to compute the entanglement in more generic (1+1)-dimensional quantum field theories (QFTs), e.g. after a quench in the sine-Gordon field theory. The study of entanglement also intertwines with another pillar of modern physics, i.e. symmetries and how their presence influences the properties of a system. Given the interest in this connection, this thesis addresses the question of how the entanglement splits into the different sectors of an internal symmetry. We approach the problem first in the QFT context, both for the free Dirac and complex scalar fields in two-dimensional spacetime, which have an abelian conserved charge, and systems having an internal Lie group symmetry to tackle the non-abelian case. Another typical framework in which we study the symmetry resolution of entanglement is lattice models, where different techniques can be exploited in order to derive exact results, ranging from the corner transfer matrix for gapped integrable systems to the connection between quadratic lattice Hamiltonians and their two-point correlation functions. The symmetry resolution also concerns other entanglement measures, namely, we analyse the behaviour of the operator entanglement, i.e. a key quantifier of the complexity of an operator, the symmetry-resolved mutual information, the effect of symmetries on entanglement negativity. The latter quantity is a genuine measure of quantum correlations in mixed states and a consistent part of the thesis is about this subject. For example, we study its time evolution after a quench and we provide an operatorial characterisation for entanglement in mixed states, which we dub negativity Hamiltonian.
Due to their great importance, both from the fundamental and from the practical points of view, it is imperative that the various facets of the concepts of information and entanglement are explored systematically in connection with diverse physical systems and processes. These concepts are at the core of the emerging field of the Physics of Information. In this Thesis I investigate some aspects of the dynamics of information in both classical and quantum mechanical systems and then move on to explore entanglement in fermion systems by searching for novel ways to classify and quantify entanglement in fermionic systems. In Chapter 1 a brief review of the different information and entropic measures as well as of the main evolution equations of classical dynamical and quantum mechanical systems is given. The conservation of information as a fundamental principle both at the classical and quantum levels, and the implications of Landauer's theorem are discussed in brief. An alternative and more intuitive proof of the no-broadcasting theorem is also provided. Chapter 2 is a background chapter on quantum entanglement, where the differences between the concept of entanglement in systems consisting of distinguishable subsystems and the corresponding concept in systems of identical fermions are emphasized. Different measures of entanglement and relevant techniques such as majorization, are introduced. To illustrate some of the concepts reviewed here I discuss the entanglement properties of an exactly soluble many-body model which was studied in paper (E) of the publication list corresponding to the present Thesis. An alternative approach to the characterization of quantum correlations, based on perturbations under local measurements, is also briefly reviewed. The use of uncertainty relations as entanglement indicators in composite systems having distinguishable subsystems is then examined in some detail. Chapter 3 is based on papers (A) and (B) of the list of publications. Extended Landauer-like principles are developed, based amongst others on the conservation of information of divergenceless dynamical systems. Conservation of information within the framework of general probabilistic theories, which include the classical and quantum mechanical probabilities as particular instances, is explored. Furthermore, Zurek's information transfer theorem and the no-deleting theorem are generalized. Chapter 4 is based on articles (C) and (D) mentioned in the publication list, and investigates several separability criteria for fermions. Criteria for the detection of entanglement are developed based either on the violation of appropriate uncertainty relations or on inequalities involving entropic measures. Chapter 5 introduces an approach for the characterization of quantum correlations (going beyond entanglement) in fermion systems based upon the state disturbances generated by the measurement of local observables. Chapter 6 summarizes the conclusions drawn in the previous chapters. The work leading up to this Thesis has resulted in five publications in peer reviewed science research journals.