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We discuss a class of quantum speed limits (QSLs) based on unified quantum($\alpha,\mu$)-entropy for nonunitary physical processes. The bounds depend onboth the Schatten speed and the smallest eigenvalue of the evolved state, andthe two-parametric unified entropy. We specialize these results to quantumchannels and non-Hermitian evolutions. In the first case, the QSL depends onthe Kraus operators related to the quantum channel, while in the second casethe speed limit is recast in terms of the non-Hermitian Hamiltonian. Toillustrate these findings, we consider a single-qubit state evolving under the(i) amplitude damping channel, and (ii) the nonunitary dynamics generated by aparity-time-reversal symmetric non-Hermitian Hamiltonian. The QSL is nonzero atearlier times, while it becomes loose as the smallest eigenvalue of the evolvedstate approaches zero. Furthermore, we investigate the interplay betweenunified entropies and speed limits for the reduced dynamics of quantummany-body systems. The unified entropy is upper bounded by the quantumfluctuations of the Hamiltonian of the system, while the QSL is nonzero whenentanglement is created by the nonunitary evolution. Finally, we apply theseresults to the XXZ model and verify that the QSL asymptotically decreases asthe system size increases. Our results find applications to nonequilibriumthermodynamics, quantum metrology, and equilibration of many-body systems.

Unified entropies and quantum speed limits for nonunitary dynamics