Luc Vinet, Alexei Zhedanov
The natural notion of almost perfect state transfer (APST) is introduced. 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 those for perfect state transfer (PST) and moreover accommodates the unavoidable imperfection of PST devices. Some examples are discussed.
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http://arxiv.org/abs/1205.4680
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