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 ...

Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta [4] are extended in terms of the parameter of the Tsallis relative operator entropy. Moreover the generalized Tsallis relative operator entropy is introduced and then several operator inequalities are derived.

Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta [5] are extended in terms of the parameter of the Tsallis relative operator entropy. Moreover the generalized Tsallis relative operator entropy is introduced and then several operator inequalities are derived.

Automatic facial recognition has many potential applications in different areas of humancomputer interaction. However, they are not yet fully realized due to the lack of an effectivefacial feature descriptor. In this paper, we present a new appearance based feature descriptor,the local directional pattern (LDP), to represent facial geometry and analyze its performance inrecognition. An LDP feat...

We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimen...