TY - JOUR

T1 - How long can it take for a quantum channel to forget everything?

AU - Ahlbrecht, Andre

AU - Richter, Florian

AU - Werner, Reinhard F.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1142/S0219749912500578

DO - 10.1142/S0219749912500578

M3 - Article

VL - 10

SP - 1250057

JO - Int. J. Quant. Inf.

JF - Int. J. Quant. Inf.

ER -