Strong converse for the quantum capacity of the erasure channel for almost all codes

Understand

A strong converse theorem for channel capacity establishes that the error probability in any communication scheme for a given channel necessarily tends to one if the rate of communication exceeds the channel's capacity.

• Establishing such a theorem for the quantum capacity of degradable channels has been an elusive task, with the strongest progress so far being a so-called "pretty strong converse".
• In this work, Morgan and Winter proved that the quantum error of any quantum communication scheme for a given degradable channel converges to a value larger than $1/\sqrt{2}$ in the limit of many channel uses if the quantum rate of communication exceeds the channel's quantum capacity.
• The present paper establishes a theorem that is a counterpart to this "pretty strong converse".