  The well-known Schmidt decomposition, or equivalently, the complex singular
value decomposition, states that a pure quantum state of a bipartite system can
always be brought into a "diagonal" form using local unitary transformations.
In this work we consider a finite-dimensional closed bipartite system with fast
local unitary control. In this setting one can define a reduced control system
on the singular values of the state which is equivalent to the original control
system. We explicitly describe this reduced control system and prove
equivalence to the original system. Moreover, using the reduced control system,
we prove that the original system is controllable and stabilizable and we
deduce quantum speed limits. We also treat the fermionic and bosonic cases in
parallel, which are related to the Autonne-Takagi and Hua factorization
respectively.
