On the quantum complexity of approximating median of continuous distribution

We consider approximating of the median of absolutely continuous distribution given by a probability density function $f$. We assume that $f$ has $r$ continuous derivatives, with derivative of order $r$ being H"older continuous with the exponent $\rho$. We study the $ϵ$-complexity of this problem in the quantum setting. We show that the $ϵ$-complexity up to logarithmic factor is of order ${ϵ}^{-1\mathrm{/}((r+\rho +1))}$.