Related papers: Reachability in Infinite Dimensional Unital Open Q…
Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets…
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
In view of controlling finite dimensional open quantum systems, we provide a unified Lie-semigroup framework describing the structure of completely positive trace-preserving maps. It allows (i) to identify the Kossakowski-Lindblad…
We examine the time discretization of Lindblad master equations in infinite-dimensional Hilbert spaces. Our study is motivated by the fact that, with unbounded Lindbladian, projecting the evolution onto a finite-dimensional subspace using a…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master…
The objective of this article is to complete preliminary results concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by Lindblad equations. The extremal system is described by a…
The reachable set for a finite dimensional quantum system is shown to be the orbit of the group corresponding to the internal and control Hamiltonians, even if this group is not compact.
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a…
We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrodinger equation. For a class of…
Quantum gates (unitary gates) on physical systems are usually implemented by controlling the Hamiltonian dynamics. When full descriptions of the Hamiltonians parameters is available, the set of implementable quantum gates is easily…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
Quantum control of an open system is demonstrated employing a thermodynamically consistent master equation. In this framework, the open system dynamics depend on the control protocol due to the dressing of the system by the drive. This…
In this study, we address the challenge of controlling quantum systems under environmental influences using the theory of dynamical invariants. We employ a reverse engineering approach to develop control protocols designed to be robust…
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and…
We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature $T>0$. We show that for fixed, small values of the coupling constant $\lambda$, the true reduced dynamics of the system is…