arXiv subjects

Domenico D'Alessandro

Publications and source records attributed to Domenico D'Alessandro.

41 records · Page 3Linked to original sources

arXiv2003

Model identification for spin networks

We consider the problem of determining the unknown parameters of the Hamiltonian of a network of spin 1/2 particles. In particular, we study experiments in which the system is driven by an externally applied electro-magnetic field and the expectation value of the total magnetization is measured. Under appropriate assumptions, we prove that, if it is possible to prepare the system in a known initial state, the above experiment allows to identify the parameters of the Hamiltonian. In the case where the initial state is itself an unknown parameter, we characterize all the pairs Hamiltonian-Initial State which give the same value of the magnetization for every form of the driving electro-magnetic field. The analysis is motivated by recent results on the isospectrality of Hamiltonians describing Magnetic Molecules.

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arXiv2003

Controllability, Observability and Parameter Identification of two coupled spin 1's

In this paper, we study the control theoretic properties of a couple of interacting spin 1's driven by an electro-magnetic field. In particular, we assume that it is possible to observe the expectation value of the total magnetization and we study controllability, observability and parameter identification of these systems. We give conditions for controllability and observability and characterize the classes of equivalent models which have the same input-output behavior. The analysis is motivated by the recent interest in three level systems in quantum information theory and quantum cryptography as well as by the problem of modeling molecular magnets as spin networks.

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arXiv2003

On Quantum State Observability and Measurement

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 the dynamics by generating all the unitary evolutions in a Lie group. We investigate to what extent, by an appropriate sequence of evolutions and measurements, we can obtain information on the initial state of the system. We present a system theoretic viewpoint of this problem in that we study the {\it observability} of the system. In this context, we characterize the equivalence classes of indistinguishable states and propose algorithms for state identification.

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arXiv2003

The Lie Algebra Rank Condition for Non-Bilinear Quantum System

The controllability condition for finite dimensional quantum systems, the Lie Algebra Rank Condition, has been stated assuming that the right invariant differential system under consideration is bilinear. We remark that this assumption is not necessary and discuss the extension to the general case.

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arXiv2001

Optimal Evaluation of Generalized Euler Angles with Applications to Classical and Quantum Control

Given two linearly independent matrices in $so(3)$, $Z_1$ and $Z_2$, every rotation matrix $X_f \in SO(3)$ can be written as the product of alternate elements from the one dimensional subgroups corresponding to $Z_1$ and $Z_2$, namely $X_f=e^{Z_1 t_1}e^{Z_2 t_2}e^{Z_1t_3} \cdot \cdot \cdot e^{Z_1t_s}$. The parameters $t_i$, $i=1,...,s$ are called {\it generalized Euler angles}. In this paper, we evaluate the minimum number of factors required for the factorization of $X_f \in SO(3)$, as a function of $X_f$, and provide an algorithm to determine the generalized Euler angles explicitly. The results can be applied to the bang bang control with minimum number of switches of some classical control systems and of two level quantum systems.

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