Related papers: Quantum Dynamics: A Dilation-Based Approach
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
This dissertation presents investigations on dynamics of discrete-time quantum walk and some of its applications. Quantum walks has been exploited as an useful tool for quantum algorithms in quantum computing. Beyond quantum computational…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their technological exploitation . A central question in…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same…
Simulation of non-adiabatic dynamics of a quantum system coupled to dissipative environments poses significant challenges. New sophisticated methods are regularly being developed with an eye towards moving to larger systems and more…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or…
We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a…
The evolution of a quantum system interacting with an environment can be described as a unitary process acting on both the system and the environment. In this framework, the system's evolution can be predicted by tracing out the…
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all…
These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…
A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most…
Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…