*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