2012/05/03 by Ahlbrecht, Andre, Richter, Florian, Werner, Reinhard F.
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1205.0693
We investigate quantum channels, which after a finite number k of repeated applications erase all input information, i.e., channels whose k-th 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.