November 8th, 2023
Nilanjana Datta (University of Cambridge)
Universal proofs of entropic continuity bounds via majorization flow
Abstract: We employ majorization theory to obtain a powerful tool for deriving simple and universal proofs of continuity bounds for various entropies which are relevant in information theory. In obtaining this, we first state a more general result which may be of independent interest: a necessary and sufficient condition under which a state maximizes a concave, continuous, Gateaux-differentiable function in an epsilon-ball in trace distance. Examples of such a function include the von Neumann entropy, Renyi entropies, and the conditional entropy. In particular, by introducing a notion of majorization flow, we prove that the alpha-Rényi entropy is Lipschitz continuous, for alpha greater than 1, thus resolving an open problem and providing a substantial improvement over previously known bounds. This is joint work with Eric Hanson.
December 13, 2023
Marco Merkli (Memorial University of Newfoundland)
TBA
TBA
January 10th, 2024
Hal Tasaki (Gakushuin University)
TBA
TBA
