Abstract
We investigate the influence of environment noise on the control cost and the quantum speed limit time (QSLT) in the process of almost exact state transmission (AEST) through a spin chain under pulse control. The chain is immersed in its surrounding non-Markovian, finite temperature heat baths. We find that AEST can be realized in weak system-bath coupling, low temperature, and strong non-Markovian baths under effective external control. Correspondingly, the control cost and QSLT increases with increasing bath temperature and coupling strength. It is noticeable that non-Markovianity from the baths can be helpful to reduce the control cost and shorten the QSLT. Furthermore, we find that there exists a trade-off between the control cost and transmission fidelity and higher fidelity requires higher cost. In addition, the minimum control cost has been found to obtain certain transmission fidelity.
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