Nilanjana Datta, University of Cambridge, U.K.
The task of determining whether a given quantum channel has a positive capacity to transmit quantum information is a fundamental open problem in quantum information theory. Using elementary techniques from analytic perturbation theory of Hermitian matrices, we devise a simple strategy to detect positive quantum capacities of quantum channels and their complements. We exhibit the utility of our method by analysing some noteworthy examples of quantum channels, such as the depolarizing- and transpose-depolarizing channels (including the Werner-Holevo channel), Hadamard channels, multi-level amplitude damping channels etc. This is joint work with Satvik Singh. Link to the arXiv posting: https://arxiv.org/abs/2105.06327