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Summary: Representing multiqubit unitary evolutions via Stokes tensors
Claudio Alta ni
SISSA-ISAS
International School for Advanced Studies
via Beirut 2-4, 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 in nitesimal 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 in nitesimal
correlation are highlighted simultaneously and can be used constructively for qubit manipulation.
For example, it allows to compute explicitly a Rodrigues' formula for the one-parameter 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 in nitesimal 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.,
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