Quantum Speed Limits Based on the Sharma-Mittal Entropy

TL;DR

This paper introduces a new class of quantum speed limits based on Sharma-Mittal entropy, providing bounds on evolution times for various quantum systems and dynamics, with applications in quantum information and metrology.

Contribution

It formulates quantum speed limits using Sharma-Mittal entropy applicable to finite-dimensional and many-body quantum systems, extending existing bounds to nonunitary and non-Hermitian dynamics.

Findings

QSLs derived from SME for single-qubit channels and non-Hermitian dynamics.

Application of SME-based QSLs to the XXZ spin chain model.

Characterization of fundamental limits on quantum evolution speeds.

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.