Related papers: Reachability in Infinite Dimensional Unital Open Q…
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…
Within a unified framework, we reveal that the seemingly disparate control approaches for classical and quantum continuous-variable systems are interconnected via differential manifolds of the ancillary representations. For classical…
We study reachable sets of open n-qubit quantum systems, whose coherent parts are under full unitary control, by adding as a further degree of incoherent control switchable Markovian noise on a single qubit. In particular, adding bang-bang…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
We discuss the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. The time-dependent generator of the dynamics of the system is of…
We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…
We study monitored quantum dynamics of infinite-range interacting bosonic systems in the thermodynamic limit. We show that under semiclassical assumptions, the quantum fluctuations along single monitored trajectories adopt a deterministic…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed.…
Quantum speed limit (QSL) is a fundamental concept in quantum mechanics and provides a lower bound on the evolution time. The attainability of QSL, greatly depending on the understanding of QSL, is a long-standing open problem especially…
Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity…
This note presents an example of bilinear conservative system in an infinite dimensional Hilbert space for which approximate controllability in the Hilbert unit sphere holds for arbitrary small times. This situation is in contrast with the…
The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus…
We study composite open quantum systems with a finite-dimensional state space ${\mathcal H}_A\otimes {\mathcal H}_B$ governed by a Lindblad equation $\rho'(t) = {\mathcal L}_\gamma \rho(t)$ where ${\mathcal L}_\gamma\rho = -i[H,\rho] +…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the…
Open Markovian quantum systems with fast and full Hamiltonian control can be reduced to an equivalent control system on the standard simplex modelling the dynamics of the eigenvalues of the density matrix describing the quantum state. We…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…