Related papers: Long-range level correlations in quantum systems w…

We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. It is known that a non-Hermitian critical point is equal to the inverse localization length of a…

The ability to measure single quanta has allowed complete characterization of small quantum systems such as quantum dots in terms of statistics of detected signals known as full-counting statistics. Quantum gas microscopy enables one to…

Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have great impact on eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal…

Multipartite quantum states saturating the Heisenberg limit of sensitivity typically require full-body correlators to be prepared. On the other hand, experimentally practical Hamiltonians often involve few-body correlators only. Here, we…

We replace a Hamiltonian with a modular Hamiltonian in the spectral form factor and the level spacing distribution function. This study establishes a connection between quantities within Quantum Entanglement and Quantum Chaos. To have a…

From the random matrix theory all the energy levels should be strongly correlated due to the presence of all off-diagonal entries.In this work we introduce two new statistics to more accurately characterize these long-distance interactions…

The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…

Spin models featuring infinite-range, homogeneous all-to-all interactions can be efficiently described due to the existence of a symmetry-restricted Hilbert subspace and an underlying classical phase space structure. However, when the…

Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…

Controlling non-equilibrium quantum dynamics in many-body systems is an outstanding challenge as interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We experimentally investigate non-equilibrium…

Knowledge of all correlation functions of a system is equivalent to solving the corresponding many-body problem. Already a finite set of correlation functions can be sufficient to describe a quantum many-body system if correlations…

We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…

Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…

Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly…

We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…

Measurements profoundly impact quantum systems, and can be used to create novel states of matter out of equilibrium. We investigate the multipartite entanglement structure that emerges in hybrid quantum circuits involving unitaries and…

Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a…

Hilbert space fragmentation provides a mechanism to break ergodicity in closed many-body systems. Here, we propose a feasible scheme to explore this exotic paradigm on a Rydberg quantum simulator. We show that the Rydberg Ising model in the…