Seminar featuring Vikesh Siddhu
A long standing issue in quantum information theory is to understand the quantum capacity. One main reason for our lack of understanding is the non-additivity of the one-shot quantum capacity. Another reason is the absence of clarity about noisy quantum channels that have positive quantum capacity.
We introduce a complementary pair of channels, each of which generalizes the quantum erasure channel. One channel in this pair produces simple instances of non-additivity of the one-shot quantum capacity. The other channel shows surprising behaviour concerning the positivity of the one-shot quantum capacity.
We also present a new method based on logarithmic singularities of the von-Neumann entropy. Using this log singularity method, we find a new type of non-additivity where using two very simple channels in parallel, one that doesn't have quantum capacity and a second that has positive one-shot quantum capacity, produces a channel whose one-shot quantum capacity exceeds that of the second channel. Another application of this method extends results of Leung and Watrous'17 concerning the positivity of the one-shot quantum capacity of qubit input channels.
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