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Quantum speed limit for arbitrary initial states
Yingjie Zhang, Wei Han, Yunjie Xia, Junpeng Cao, Heng Fan
TL;DR
The paper seeks a general quantum speed-limit bound for open-system evolution from arbitrary initial states. It derives a relative-purity-based bound and finds distinct temporal behaviors in damped Jaynes–Cummings and Ohmic-like dephasing models.
Problem
A general quantum speed-limit bound is needed for open systems evolving from arbitrary mixed or pure initial states.
Method
The authors use relative purity as a distance measure to derive unified Margolus–Levitin- and Mandelstam–Tamm-type bounds for arbitrary mixed initial states.
Results
The bound decreases then increases in Markovian damped Jaynes–Cummings dynamics, oscillates periodically in the non-Markovian regime, and approaches a fixed value for super-Ohmic dephasing.
Takeaways & Limitations
The resulting quantum speed-limit time characterizes speed changes for time-dependent states in noisy open-system dynamics.
Abstract
from arXiv · showhide
We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.