Classical, i.e. non-quantum, blind source separation (BSS) methods estimate unknown source signals by using only mixed signals obtained by transferring these source signals through a mixing transform, which typically has unknown parameter values. We developed quantum versions of BSS, in which the mixing parameter values almost always remained fixed over time. We here show that rapidly varying mixing is much more complex to handle, because unknown quantum states cannot be cloned, i.e. copied. We avoid this issue thanks to a specific separating system based on a master-slave structure. We provide an original analytical analysis of the performance of that structure, depending on the mismatch between its master and slave inverting blocks.