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CATEGORIES:Information Theory Seminar
SUMMARY:Uniform entropic continuity bounds via majorizatio
n flow - Prof. Nilanjana Datta\, University of Cam
bridge
DTSTART;TZID=Europe/London:20221130T140000
DTEND;TZID=Europe/London:20221130T150000
UID:TALK182564AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/182564
DESCRIPTION:We employ majorization theory to obtain a powerful
tool for deriving simple and universal proofs\nof
continuity bounds for various entropies which are
relevant in classical and quantum information the
ory. \nIn obtaining this\, we first derive a more
general result which may be of independent interes
t: a necessary and sufficient condition under whic
h a state maximizes a concave\, continuous\, Gatea
ux-differentiable function in an epsilon-ball in t
race distance. Examples of such a function include
the von Neumann entropy\, Renyi entropies\, and t
he conditional entropy. In particular\, by introdu
cing a notion of majorization flow\, we prove that
the alpha-Rényi entropy is Lipschitz continuous\,
for alpha > 1\, thus resolving an open problem an
d providing a substantial improvement over previou
sly known bounds. We also discuss some challenging
open questions. This is joint work with Eric Hans
on. Note that no prior knowledge in\nquantum infor
mation theory is required to understand the talk.
LOCATION:MR5\, CMS Pavilion A
CONTACT:Dr Varun Jog
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