Almost perfect state transfer in quantum spin chains

Abstract

The natural notion of almost perfect state transfer (APST) is examined. It is applied to the modelling of efficient quantum wires with the help of $XX$ spin chains. It is shown that APST occurs in mirror-symmetric systems, when the 1-excitation energies of the chains are linearly independent over rational numbers. This result is obtained as a corollary of the Kronecker theorem in Diophantine approximation. APST happens under much less restrictive conditions than perfect state transfer (PST) and moreover accommodates the unavoidable imperfections. Some examples are discussed.