Related papers: Quantum Control and Representation Theory
This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer…
A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
A New theoretical formalism for the optimal quantum control has been presented. The approach stems from the consideration of describing the time-dependent quantum system in terms of the real physical observables, viz., the probability…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability…
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
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…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
In this paper we attempt to provide a physical representation of quantum superpositions. For this purpose we discuss the constraints of the quantum formalism to the notion of possibility and the necessity to consider a potential realm…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
This paper explains some fundamental ideas of {\em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and…
The extraordinary success in laser cooling, trapping, and coherent manipulation of atoms has energized the efforts in extending this exquisite control to molecules. Not only are molecules ubiquitous in nature, but the control of their…
The theory of controlled quantum open systems describes quantum systems interacting with quantum environments and influenced by external forces varying according to given algorithms. It is aimed, for instance, to model quantum devices which…
In the design of complex quantum systems like ion traps for quantum computing, it is usually desired to stabilize a particular system state or make the system state track a desired trajectory. Several control theoretical approaches based on…
Feynman, in 1982, proposed the idea of using a quantum simulator to perform quantum simulations. A quantum simulator is basically a controllable quantum system that can mimic the dynamics of other quantum systems we wish to study. In this…