  Relaxation effects impose fundamental limitations on our ability to
coherently control quantum mechanical phenomena. In this letter, we establish
physical limits on how closely can a quantum mechanical system be steered to a
desired target state in the presence of relaxation. In particular, we
explicitly compute the maximum coherence or polarization that can be
transferred between coupled nuclear spins in the presence of very general
decoherence mechanisms that include cross-correlated relaxation. We give
analytical expressions for the control laws (pulse sequences) which achieve
these physical limits and provide supporting experimental evidence.
Exploitation of cross-correlation effects has recently led to the development
of powerful methods in NMR spectroscopy to study very large biomolecules in
solution. We demonstrate with experiments that the optimal pulse sequences
provide significant gains over these state of the art methods, opening new
avenues for spectroscopy of much larger proteins. Surprisingly, in spite of
very large relaxation rates, optimal control can transfer coherence without any
loss when cross-correlated relaxation rates are tuned to auto-correlated
relaxation rates.
