  We consider an exact state swap, defined as the swap between two quantum
states |A> and |B> in the Hilbert space of a quantum system. We show that,
given an arbitrary Hamiltonian dynamics, there is a straightforward approach to
calculating the probability of the occurrence of an exact state swap, by
employing an exchange operator P_{AB}. For a given dynamics, the feasibilities
of proposed quantum setups, such as quantum state amplifications and transfers
can be evaluated. These setups are only distinguished by different forms of
P_{AB}, which easily lead to innovative designs of quantum setups or devices.
We illustrate the method with the isotropic XY model, whose unnoticed features
are revealed.

Quantum Physics