The search for fast unitary transforms and the need for data compression in linear systems are complementary issues. Compression requires the definition of a threshold dependent on the condition number, which is invariant over the unitary group. With respect tot this threshold it is shown that the SVD is the optimal tool. Considerations in connection with the Kronecker product and direct sum of...

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices of a unitary representation to canonical form, give a certain description of the representations of canonical form, and reduce the problem of classifying Eu...

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial st...

This article concerns the exact controllability of unitary groups on Hilbert spaces with unbounded control operator. It provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality. By the transmutation of controls in some time L for the corresponding second order conservative system, it is proved that the cost of controls in...

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption whose validity is not obvious. We introduce two different schemes by which any arbitrary unitary time evolution and measurement can be implemented with desire...

This is a challenging paper including some review and new results. Since the non–commutative version of the classical system based on the compact group SU(2) has been constructed in (quant-ph/0502174) by making use of Jaynes–Commings model and so–called Quantum Diagonalization Method in (quant-ph/0502147), we construct a non–commutative version of the classical system based on the non–compact g...