Quantum Speed Limit and Optimal Evolution Time in Driven-dissipative Systems

Abstract:Quantum Speed Limit (QSL) is a lower bound on the evolution time $T_{\rm QSL}$ of a closed quantum system to evolve from one state to another, as shown by Mandelstam and Tamm. For a driving Hamiltonian enforcing the evolution, the time-energy uncertainty relations for the drive play the dominant role in setting the bound. On the other hand, dissipative systems can also suffer from drive-induced dissipation (DID). In this work, we ask how DID modifies the attainability of the QSL in open quantum systems and whether the time-energy uncertainty relation remains the dominating factor. For open quantum systems that suffer from DID, we report a finite optimal evolution time $T_{\rm DID} \; (> T_{\rm QSL})$ for constant-amplitude driving. We show that the competition between DID at short times and environmental dissipation at long times produces a non-monotonic dependence of fidelity on the evolution time. When the drive waveform is shaped using quantum optimal control (QOC), an intermediate attainable evolution time $T_{\rm QOC}$ provides the maximum fidelity. Our results therefore suggest that, in driven-dissipative systems, the conventional QSL lower bound should be complemented by a finite-time attainability window determined by dissipation, with $T_{\rm QSL} \le T_{\rm QOC} \le T_{\rm DID}$ for the cases studied here. Further, we show that the optimized control protocol is robust against detuning and variations in environmental parameters, enabling reliable quantum control in open systems and providing a practical route toward high-fidelity state transfer in two-level quantum systems.

arXiv:2504.07931 [quant-ph]

(or arXiv:2504.07931v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2504.07931 Focus to learn more arXiv-issued DOI via DataCite

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