Abstract
We investigate quantum channels, which after a finite number k of repeated applications erase all input information, i.e. channels whose kth power (but no smaller power) is a completely depolarizing channel. We show that on a system with Hilbert space dimension d, the order is bounded by k ≤ d2 - 1, and give an explicit construction scheme for such channels. We also consider strictly forgetful memory channels, i.e. channels with an additional input and output in every step, which after exactly k steps retain no information about the initial memory state. We establish an explicit representation for such channels showing that the same bound applies for the memory depth k in terms of the memory dimension d.
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