Related papers: Quantum Control and Representation Theory
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 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…
It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of…
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…
We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…
This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics,…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…
Control theory concerns with the question if and how it is possible to drive the behavior of a complex dynamical system. A system is said to be controllable if we can drive it from any initial state to any desired final state in finite…
In this work we focus on a recently introduced method [1] to construct the external potential $v$ that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. We show how this…
It is well-known that any compact Lie group appears as closed subgroup of a unitary group, $G\subset U_N$. The unitary group $U_N$ has a free analogue $U_N^+$, and the study of the closed quantum subgroups $G\subset U_N^+$ is a problem of…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol.…
Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
In control theory, researchers need to understand a system's local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space…