Hamiltonians that realize perfect quantum state transfer and early state exclusion

Abstract

In this paper, we show how to construct XX Hamiltonians that realize perfect quantum state transfer and also have the property that the overlap of the time evolved state with the initial state is zero for some time before the transfer time. If the latter takes place, we call it an early exclusion state. We also show that in some cases, early state exclusion is impossible. The proofs rely on properties of Krawtchouk and Chebyshev polynomials.