1106.2337 (Yingkai Ouyang)

Upper Bounds on the Quantum Capacity of the Depolarizing Channel with
Higher Dimension Amplitude Damping Channels    [PDF]

Yingkai Ouyang

Evaluating the quantum capacity of the quantum channels is an important
problem. Depolarizing channels are an important family of quantum channels.
However the quantum capacity of depolarizing channels do not have tight
numerical bounds. Smith and Smolin have previously obtained the best known
upper bounds on the quantum capacity of the qubit depolarizing channels using
degradable extensions of quantum channels, with the entire family of degradable
qubit channels as the main ingredient. We use the same method as Smith and
Smolin but with a different main ingredient -- a special family of degradable
two-qubit channels -- to obtain upper bounds on the four-dimension depolarizing
channel. We use our special ingredient to obtain upper bounds on the qubit
depolarizing channel, but find no improvement over Smith and Smolin's upper
bound. We also prove sufficient conditions for which the quantum capacity of a
quantum channel may be evaluated by optimizing its coherent information over
diagonal states, and prove that our special family of channels has this
property. With Smith and Smolin's method, we also show that Pauli-twirling of
some of our special channels strictly decreases the quantum capacity, but we do
not know if further Clifford-twirling also strictly reduces the quantum
capacity.

View original: http://arxiv.org/abs/1106.2337