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SUMMARY:Uniform entropic continuity bounds via majorization flow - Prof. N
 ilanjana Datta\, University of Cambridge
DTSTART:20221130T140000Z
DTEND:20221130T150000Z
UID:TALK182564@talks.cam.ac.uk
CONTACT:Dr Varun Jog
DESCRIPTION:We employ majorization theory to obtain a powerful tool for de
 riving simple and universal proofs\nof continuity bounds for various entro
 pies which are relevant in classical and quantum information theory. \nIn 
 obtaining this\, we first derive a more general result which may be of ind
 ependent interest: a necessary and sufficient condition under which a stat
 e maximizes a concave\, continuous\, Gateaux-differentiable function in an
  epsilon-ball in trace distance. Examples of such a function include the v
 on Neumann entropy\, Renyi entropies\, and the conditional entropy. In par
 ticular\, by introducing a notion of majorization flow\, we prove that the
  alpha-Rényi entropy is Lipschitz continuous\, for alpha > 1\, thus resol
 ving an open problem and providing a substantial improvement over previous
 ly known bounds. We also discuss some challenging open questions. This is 
 joint work with Eric Hanson. Note that no prior knowledge in\nquantum info
 rmation theory is required to understand the talk.
LOCATION:MR5\, CMS Pavilion A
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