Quantum speed limit

Zi-yi Mai, Zheng Liu, Chang‐shui Yu

We propose a quantum state distance and develop a family of geometrical quantum speed limits (QSLs) for open and closed systems. The QSL time includes an alternative function by which we derive three QSL times with particularly chosen functions. It indicates that two QSL times are exactly the ones presented in Ref. \cite{Campaioli2019tightrobust} and \cite{mai2023tight}, respectively, and the third one can provide a unified QSL time for both open and closed systems. The three QSL times are attainable for any given initial state in the sense that there exists a dynamics driving the initial state to evolve along the geodesic. We numerically compare the tightness of the three QSL times, which typically promises a tighter QSL time if optimizing the alternative function.

Durrani, Ijaz

Soroush Haseli, S. Salimi

Abstract The minimum time a system needs to change from an initial state to a final orthogonal state is called the quantum speed limit time. The quantum speed limit time can be used to quantify the speed of the quantum evolution. The speed of the quantum evolution will increase, if the quantum speed limit time decreases. In this work, we will use a relative purity-based bound for the quantum speed limit time. This work is applicable for any arbitrary initial state. Here, we investigate the effects of a filtering operation on the quantum speed limit time. It will be observed that for some intervals of the filtering operation parameter, the quantum speed limit time is decreased by increasing the filtering operation parameter and for some other intervals it is decreased by decreasing the filtering operation parameter.

K. Kobayashi, Naoki Yamamoto

In this paper we propose to use a quantum speed limit (QSL) as a measure of robustness of states, defining a state with a bigger QSL as more robust. From this perspective, it is important to have an explicitly computable QSL, because then we can formulate an engineering problem of the Hamiltonian that makes a target state robust against decoherence. Hence we derive an explicitly computable QSL that is applicable to general Markovian open quantum systems. This QSL is tighter than another explicitly computable QSL, in an important setup such that decoherence is small. Also, the Hamiltonian engineering problem with this QSL is a quadratic convex optimization problem, and thus it is efficiently solvable. The idea of robust state characterization and the Hamiltonian engineering, in terms of the QSL, is demonstrated with several examples.

Nicoletta Carabba