Quantum flags, and new bounds on the quantum capacity of the depolarizing channel

Understand

A new bound for the quantum capacity of the $d$-dimensional depolarizing channels is presented.

• Our derivation makes use of a flagged extension of the map where the receiver obtains a copy of a state $\sigma_0$ whenever the messages are transmitted without errors, and a copy of a state $\sigma_1$ when instead the original state gets fully depolarized.
• By varying the overlap between the flags states, the resulting transformation nicely interpolates between the depolarizing map (when $\sigma_0=\sigma_1$), and the $d$-dimensional erasure channel (when $\sigma_0$ and $\sigma_1$ have orthogonal support).
• In our analysis we compute the product-state classical capacity, the entanglement assisted capacity and, under degradability conditions, the quantum capacity of the flagged channel.