Control cost and quantum speed limit time in controlled almost exact state transmission in open systems

TL;DR

This paper studies how environment noise affects control cost and quantum speed limits in nearly perfect state transmission through a spin chain, revealing the roles of bath properties and non-Markovianity.

Contribution

It demonstrates the conditions for achieving almost exact state transmission in open systems and analyzes the impact of bath characteristics on control cost and speed limits.

Findings

Non-Markovian baths help reduce control cost and QSLT.

Higher temperature and coupling increase control cost and QSLT.

Trade-off exists between transmission fidelity and control cost.

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.