Related papers: Small time reachable set of bilinear quantum syste…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems…
We consider the Schr\"odinger partial differential equation of a rotating symmetric rigid molecule (symmetric rotor) driven by a z-linearly polarized electric field, as prototype of degenerate infinite-dimensional bilinear control system.…
In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We…
This paper investigates the optimal control of a bilinear damped wave equation over an infinite time horizon. We establish the well-posedness of the controlled system and derive uniform energy estimates. The existence of optimal controls is…
In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…
We analyze the possibility and efficiency of non-holonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary…
It is shown that the order property of pure bipartite states under SLOCC (stochastic local operations and classical communications) changes radically when dimensionality shifts from finite to infinite. In contrast to finite dimensional…
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…
In quantum control theory, the fundamental issue of controllability covers the questions whether and under which conditions a system can be steered from one pure state into another by suitably tuned time evolution operators. Even though Lie…
In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne…
We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
It was shown in arXiv:0906.2527, that in finite-dimensional Hilbert spaces each operator system corresponds to some channel, for which this operator system will be an operator graph. This work is devoted to finding necessary and sufficient…
We derive sufficient conditions for infinite-dimensional systems whose entanglement is not completely lost in a finite time during its decoherence by a passive interaction with local vacuum environments. The sufficient conditions allow us…
We investigate accessibility and controllability of a quantum system S coupled to a quantum probe P, both described by two-dimensional Hilbert spaces, under the hypothesis that the external control affects only P. In this context…
Quantum gravitational effects suggest a minimal length, or spacetime interval, of order the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with…
We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…
The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection…