Figure 1

Revivals of distance and entropic distinguishability quantifiers versus their bounds for the two models considered in Sec. 5, namely, (a) and (b) the spin-star dephasing model with $N=5$ environmental qubits and random coupling strengths and (c) and (d) the Jaynes-Cummings model. (a) and (c) Behavior of the Helstrom norm $D$ [orange (light gray) lines] and the square root of the Jensen-Shannon divergence $\sqrt{J}$ [green (gray) lines], together with the Holevo ($K$) and quantum ($S$) skew divergence evaluated for $\mu =1/2$ [black (dark gray) lines] so that the latter two coincide. The solid lines represent the lhs of Eq. (48), Eq. (61), and Eqs. (41) and (57) evaluated for $\mu =1/2$ and $t=T$, respectively. The dotted lines denote the sum of the corresponding contributions on the rhs. (b) and (d) Behavior of Holevo skew divergence $K$ [green (gray) lines] and quantum $S$ [black (dark gray) lines] skew divergence for $\mu =1/4$. Again, solid lines correspond to the lhs of Eqs. (41) and (57), respectively, while the dotted lines reproduce the rhs. Despite the quite different nature of the two models, which describe, for a two-level system, decoherence and excitation exchanges with a bosonic mode, respectively, the overall behavior of distinguishability quantifiers and related bounds is strikingly similar. In particular, it clearly appears that distance quantifiers provide tighter bounds. For the spin-star model the reference time $T$ is equal to 5 in inverse units of the average coupling strength, while for the Jaynes-Cummings model $T$ is 8.9 in inverse units of the coupling strength $g$, while the detuning frequency $\mathrm{\Delta }$ is equal to 0.5 in units of $g$.