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arXiv · 2512.24070

Quantum Speed Limits Based on the Sharma-Mittal Entropy

Dong-Ping Xuan·Zhi-Xi Wang·Shao-Ming Fei
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Abstract

Quantum speed limits (QSLs) establish intrinsic bounds on the minimum time required for the evolution of quantum systems. We present a class of QSLs formulated in terms of the two-parameter Sharma-Mittal entropy (SME), applicable to finite-dimensional systems evolving under general nonunitary dynamics. In the single-qubit case, the QSLs for both quantum channels and non-Hermitian dynamics are analyzed in detail. For many-body systems, we explore the role of SME-based bounds in characterizing the reduced dynamics and apply the results to the XXZ spin chain model. These entropy-based QSLs characterize fundamental limits on quantum evolution speeds and may be employed in contexts including entropic uncertainty relations, quantum metrology, coherent control and quantum sensing.

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Dong-Ping Xuan, Zhi-Xi Wang, Shao-Ming Fei. 2025-12-30. Quantum Speed Limits Based on the Sharma-Mittal Entropy. https://doi.org/10.1002/andp.202500383

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