 
Summary: Representing multiqubit unitary evolutions via Stokes tensors
Claudio Altani
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
For the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit
formulation of the corresponding unitary dynamics at the innitesimal level. The main advantage
of this formalism (clearly reminiscent of the ideas of \coherences" and \coupling Hamiltonians"
of spin systems) is that the pattern of correlation between qubits and the pattern of innitesimal
correlation are highlighted simultaneously and can be used constructively for qubit manipulation.
For example, it allows to compute explicitly a Rodrigues' formula for the oneparameter orbits of
nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows
to express the Cartan decomposition of unitary propagators as a linear action directly in terms of
the innitesimal generators.
PACS numbers: 03.65.Ud, 03.67.Mn, 03.67.a
I. INTRODUCTION
The easiest and most promising type of \quantum net
work" i.e., of collection of quantum systems to be manip
ulated individually or jointly for the purposes of quantum
information processing, is by far composed of qubits i.e.,
