Quantum Speed Limits Based on the Sharma–Mittal Entropy

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.