Quantum Speed Limit for Non-Markovian Dynamics

We derive a Margolus-Levitin-type bound on the minimal evolution time of an arbitrarily driven open quantum system. We express this quantum speed limit time in terms of the operator norm of the nonunitary generator of the dynamics. We apply these results to the damped Jaynes-Cummings model and demonstrate that the corresponding bound is tight. We further show that non-Markovian effects can speed up quantum evolution and therefore lead to a smaller quantum speed limit time.

Figure 1

Quantum speed limit time ${\tau }_{\mathrm{QSL}}$, Eq. (21), for the damped Jaynes-Cummings model as a function of the coupling strength ${\gamma }_0$. The three curves are obtained for the trace norm (green dotted line), Hilbert-Schmidt norm (blue dashed line), and the operator norm (red solid) of the nonunitary generator $L({\rho }_t)$, Eq. (23). The black (dash-dotted) line represents the actual driving time $\tau =1$. Parameters are $\lambda =50$ and ${\omega }_0=1$.

Figure 2

Time-averaged operator norm of the nonunitary generator $L({\rho }_t)$ of the damped Jaynes-Cummings model (23) (continuous line). The dotted line corresponds to the Markovian result, Eq. (27). The inset shows the fidelity $F({\rho }_0,{\rho }_{\tau })=\cos (\mathcal{L}({\rho }_0,{\rho }_{\tau }))$. Same parameters as in Fig. 1.