For a right-invariant system on a compact Lie group G, I present two methods to design a control to drive the state from the identity to any element of the group. The first method, under appropriate...
I obtain the dynamics of the continuous time quantum walk on a $d$-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on...
A note on generalized concurrences and entanglement detection (2008)
Cattaneo, Laura, D'Alessandro, Domenico
We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2 X 4 states of rank 2, we prove that generalized concurrences do not,...
Lie Algebraic Analysis and Control of Quantum Dynamics (2008)
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to...
Non-stationary quantum walks on the cycle (2007)
D'Alessandro, Domenico, Parlangeli, Gianfranco, Albertini, Francesca
We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state...
A General Framework for Recursive Decompositions of Unitary Quantum Evolutions (2007)
Dagli, Mehmet, D'Alessandro, Domenico, Smith, Jonathan D. H.
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement....
Albertini, Francesca, D'Alessandro, Domenico
In this paper, we consider the problem of model equivalence for quantum systems. Two models are said to be (input-output) equivalent if they give the same output for every admissible input. In the...
Decompositions of unitary evolutions and entanglement dynamics of bipartite quantum systems (2006)
D'Alessandro, Domenico, Romano, Raffaele
We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure which systematically...
Environment induced incoherent controllability (2005)
Romano, Raffaele, D'Alessandro, Domenico
We prove that the environment induced entanglement between two non interacting, two-dimensional quantum systems S and P can be used to control the dynamics of S by means of the initial state of P....
Quantum Symmetries and Cartan Decompositions in Arbitrary Dimensions (2005)
D'Alessandro, Domenico, Albertini, Francesca
We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the...
On Quantum State Observability and Measurement (2003)
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...
Model identification for spin networks (2003)
Albertini, Francesca, D'Alessandro, Domenico
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...
Controllability, Observability and Parameter Identification of two coupled spin 1's (2003)
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...
The Lie Algebra Rank Condition for Non-Bilinear Quantum System (2003)
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...
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...
A Superposition Theorem for Solutions of the Riccati Difference Equation (1998)
We show that, given any pair of solutions of the matrix Riccati difference equation, it is possible to construct a whole family of solutions via projective superposition laws. This extends known...