Related papers: Inverse counting statistics for stochastic and ope…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of non-deterministic quantum…
Characterization and quantification of non-Markovian dynamics in open quantum systems are topical issues in the rapidly developing field of quantum computation and quantum communication. A standard approach based on the notion of…
We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by…
Quantum state tomography, a process that reconstructs a quantum state from measurements on an ensemble of identically prepared copies, plays a crucial role in benchmarking quantum devices. However, brute-force approaches to quantum state…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
We consider the full probability distribution for the transverse magnetization of a finite subsystem in the transverse field Ising chain. We derive a determinant representation of the corresponding characteristic function for general…
In this paper we develop a method to compute the solution to a countable (finite or infinite) set of equations that occurs in many different fields including Markov processes that model queueing systems, birth-and-death processes and…
We consider closed quantum many-body systems subject to stochastic resetting. This means that their unitary time evolution is interrupted by resets at randomly selected times. When a reset takes place the system is reinitialized to a state…
We put forward a novel approach to study the evolution of an arbitrary open quantum system under a resetting process. Using the framework of renewal equations, we find a universal behavior for the mean first return time that goes beyond…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator $\rho_{AB}$ of a composite system can be derived from the…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an…
We realize on an Atom-Chip a practical, experimentally undemanding, tomographic reconstruction algorithm relying on the time-resolved measurements of the atomic population distribution among atomic internal states. More specifically, we…
A two-level atom interacting with an electromagnetic mode in a cavity experiences population collapses and revivals. They are an indirect signature of the field quantization, and also hold information about the mode. Thus, they may be…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…