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For both unitary and open qubit dynamics, we compare asymmetry monotone-basedbounds on the minimal time required for an initial qubit state to evolve to afinal qubit state from which it is probabilistically distinguishable with fixedminimal error probability (i.e., the minimal error distinguishability time).For the case of unitary dynamics generated by a time-independent Hamiltonian,we derive a necessary and sufficient condition on two asymmetry monotones thatguarantees that an arbitrary state of a two-level quantum system or a separablestate of $N$ two-level quantum systems will unitarily evolve to another statefrom which it can be distinguished with a fixed minimal error probability$\delta \in [0,1/2]$. This condition is used to order the set of qubit statesbased on their distinguishability time, and to derive an optimal release timefor driven two-level systems such as those that occur, e.g., in theLandau-Zener problem. For the case of non-unitary dynamics, we compare threelower bounds to the distinguishability time, including a new type of lowerbound which is formulated in terms of the asymmetry of the uniformlytime-twirled initial system-plus-environment state with respect to thegenerator $H_{SE}$ of the Stinespring isometry corresponding to the dynamics,specifically, in terms of $\Vert [H_{SE},\rho_{\text{av}}(\tau)]\Vert_{1}$,where $\rho_{\text{av}}(\tau):={1\over \tau}\int_{0}^{\tau}dt\,e^{-iH_{SE}t}\rho \otimes \vert 0\rangle_{E}\langle 0\vert_{E} e^{iH_{SE}t}$.

Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball