IQI Weekly Seminar

Abstract:

We determine both the quantum and the private capacities of low-noise

quantum channels to leading orders in the channel's distance to the

perfect channel. It has been an open problem for more than 20 years to determine the

capacities of some of these low-noise channels such as the

depolarizing channel.  We also show that both capacities are equal to the single-letter

coherent information of the channel, again to leading orders. We thus find

that, in the low noise regime, super-additivity and degenerate codes

have negligible benefit for the quantum capacity, and shielding does

not improve the private capacity beyond the quantum capacity, in

stark contrast to the situation when noisier channels are considered.