Wenhua Wang

An upper bound for the adiabatic approximation error

In this paper, we derive an upper bound for the adiabatic approximation error, which is the distance between the exact solution to a Schrödinger equation and the adiabatic approximation solution. As an application, we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a Schrödinger equation.

Generalized Robustness of Contextuality

Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC) R C ( e ) of an empirical model e against non-contextual noises was introduced and discussed in Science China Physics, Mechanics and Astronomy (59(4) and 59(9), 2016). Because noises are not always non-contextual, this paper introduces and discusses the generalized robustness of contextuality (GRoC) R g ( e ) of an empirical model e against general noises. It is proven that R g ( e ) = 0 if and only if e is non-contextual. This means that the quantity R g can be used to distinguish contextual empirical models from non-contextual ones. It is also shown that the function R g is convex on the set of all empirical models and continuous on the set of all no-signaling empirical models. For any two empirical models e and f such that the generalized relative robustness of e with respect to f is finite, a fascinating relationship between the GRoCs of e and f is proven, which reads R g ( e ) R g ( f ) ≤ 1 . Lastly, for any n-cycle contextual box e, a relationship between the GRoC R g ( e ) and the extent Δ e of violating the non-contextual inequalities is established.

Two generalized Wigner–Yanase skew information and their uncertainty relations

In this paper, we first define two generalized Wigner–Yanase skew information

Uncertainty relations with the generalized Wigner–Yanase–Dyson skew information

|K_{\rho ,\alpha }|(A)

Computable upper bounds for the adiabatic approximation errors

|Kρ,α|(A) and

Continuity of the robustness of contextuality of empirical models

|L_{\rho ,\alpha }|(A)