Abstract: Information can be encoded in bits and sent across a noisy channel. This classical notion can be generalized using quantum theory: information can be encoded in quantum bits (qubits) and sent across a noisy quantum channel. The generalization gives a quantum theory of communication. Unlike its classical counterpart, quantum communication can be non-additive: two quantum channels used together can send information at a rate strictly larger than the sum of rates for each separate channel. This non-additivity can be harnessed to enhance quantum communication, but it can also cause difficulties. For instance non-additivity makes it hard to check if a channel's quantum capacity (a quantum generalization of the Shannon capacity) is positive.

We will present results about both positivity and non-additivity of the quantum capacity. These results include (1) a simple class of channels with non-zero quantum capacity and (2) a type of non-additivity where a quantum channel with no quantum capacity boosts quantum communication across another quantum channel. While these results reveal new and surprising ways for sending quantum information, they also raise conceptual issues about channels with no quantum capacity. Our results come from an interesting technical tool, log-singularities in the von-Neumann entropy [1], which may be of independent interest.

Knowledge of quantum theory is not required for this talk.

[1] - arxiv.org/abs/2003.10367