Quantum State Transfer in Engineered Spin Chain under Influence of Spatially Distributed Environment

It has been shown that a quantum state could be perfectly transferred via a spin chain with engineered ``always-on interaction". In this paper, we study a more realistic problem for such a quantum state transfer (QST) protocol, how the efficacy of QST is reduced by the quantum decoherence induced by a spatially distributed environment. Here, the environment is universally modeled as a bath of fermions located in different positions. By making use of the irreducible tensor method in angular momentum theory, we investigate the effect of environment on the efficiency of QST for both cases at zero and finite temperatures. We not onlyshow the generic exponential decay of QST efficiency as the number of sites increase, but also find some counterintuitive effect, the QST can be enhanced as temperature increases in some cases.