Generalized Bound on Quantum Dynamics: Efficiency of Unitary Transformations between Non-Hermitian States

We report a general bound for the efficiency of polarization or coherence transfer between quantized states under unitary transformations. This bound is more general than the so-called universal bound on spin dynamics [O. W. S{}rensen, J. Magn. Reson. 86, 435 (1990)] that applies only to transformations between Hermitian states. The new bound on transfer efficiency under unitary transformations between general non-Hermitian operators depends exclusively on the singular values of the matrix representations of these operators.