A bstract We study upper bounds on the growth of operator entropy S K in growth. Using uncertainty relation, we first prove a dispersion bound rate |∂ t | ≤ 2 b 1 ∆ , where is Lanczos coefficient and variance . However, for irreversible process, this generally turns out to be too loose at long times. further find tighter time limit using universal logarithmic relation between Krylov complexity ...

Quantifying coherence is an essential endeavor for both quantum mechanical foundations and technologies. We present a bona fide measure of by utilizing the Tsallis relative operator (α,β)-entropy. first prove that proposed fulfills all criteria well defined measure, including strong monotonicity in resource theories coherence. then study ordering (α,β)-entropy coherence, α-entropies Rényi α-ent...