Related papers: Les Houches lectures on random quantum circuits an…
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and…
Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and…
The overarching goal of this thesis is to demonstrate that complementarity is at the heart of quantum information theory, that it allows us to make (some) sense of just what information "quantum information" refers to, and that it is useful…
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient…
This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer.…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
In the standard formulation of quantum mechanics, there exists an inherent feedback of the measurement setting on the elementary object under scrutiny. Thus one cannot assume that an 'element of reality' prexists to the measurement and, it…
The education system for students in physics suffers (worldwide) from the absence of a deep course in probability and randomness. This is the real problem for students interested in quantum information theory, quantum optics, and quantum…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions…
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states describe not an absolute property of a system but rather a relationship between systems. In this article, we observe that…
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
We study information storage in noisy quantum registers and computers using the methods of statistical dynamics. We develop the concept of a strictly contractive quantum channel in order to construct mathematical models of physically…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…