Related papers: Stabilizing Open Quantum Systems by Markovian Rese…
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…
Reservoir engineering is a powerful technique to autonomously stabilize a quantum state. Traditional schemes involving multi-body states typically function for discrete entangled states. In this work, we enhance the stabilization capability…
We introduce a novel reservoir engineering approach for stabilizing multi-component Schr\"odinger's cat manifolds. The fundamental principle of the method lies in the destructive interference at crossings of gain and loss Hamiltonian terms…
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems…
This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations…
We develop a framework to analyze the dynamics of a finite-dimensional quantum system $\rm S$ in contact with a reservoir $\rm R$. The full, interacting $\rm SR$ dynamics is unitary. The reservoir has a stationary state but otherwise…
We study the dissipative stabilization of entangled states in arrays of quantum systems. Specifically, we are interested in the states of qubits (spin-1/2) which may or may not interact with one or more cavities (bosonic modes). In all…
We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: The dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator ${\cal L}$. The eigenvalues…
In quantum systems theory one of the fundamental problems boils down to: Given an initial state, which final states can be reached by the dynamic system in question? Formulated in the framework of bilinear control systems, the evolution…
We study the evolution of an open quantum system described by a dynamical semigroup having the Lindblad superoperator as a generator. This generator may have an eigenfunction with a unity eigenvalue, referred to as a constant of motion…
We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…
Quantum phase transitions are a cornerstone of many-body physics at low temperatures but have remained elusive far from equilibrium. Driven open quantum systems -- a prominent non-equilibrium platform where coherent dynamics competes with…
The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…
Reservoir computing systems are constructed using a driven dynamical system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning, and computation. A…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…
We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between…
This article concerns the attraction domain analysis for steady states in Markovian open quantum systems. The central question is proposed as: given a steady state, which part of the state space of density operators does it attract and…
Exceptional points are spectral singularities where both eigenvalues and eigenvectors collapse onto a single mode, causing the system behavior to shift abruptly and making it highly responsive to even small perturbations. Although widely…
In this paper, we study the evolution of Markovian open quantum systems, whose dynamics are governed by the von Neumann-Lindblad equations. Our goal is to prove the return-to-equilibrium property for systems of infinite degrees of freedom…