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General Quantum State Swap: an XY model analysis

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.