相关论文: Analytic Controllability of Time-Dependent Quantum…

A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…

Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited…

We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…

Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…

It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…

In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show under which conditions measurements, state preparations, and unitary implementations on the system can be performed by quantum…

A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…

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…

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…

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…

We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…

Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…

We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…

Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…

We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any…

A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realises a required quantum process or task, under the influence of a prevailing `background' Hamiltonian that cannot be manipulated. When the task…

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…

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…

We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on isolated quantum dynamics. Deterministic analog control errors are formulated as time-dependent operators in the Schrodinger equation. We…