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CATEGORIES:Information Theory Seminar
SUMMARY:From Classical to Quantum: Uniform Continuity Boun
 ds on Entropies in Infinite Dimensions - Prof. Nil
 anjana Datta\, DAMTP
DTSTART;TZID=Europe/London:20241127T140000
DTEND;TZID=Europe/London:20241127T150000
UID:TALK222169AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/222169
DESCRIPTION:  It is known that the Shannon entropy is disconti
 nuous for discrete random variables with a countab
 ly infinite alphabet. Analogously\, in the quantum
  case\, the von Neumann entropy is discontinuous f
 or quantum states on an infinite-dimensional\, sep
 arable Hilbert space. However\, continuity can be 
 restored by imposing natural constraints on the ra
 ndom variables (resp. quantum states).  We obtain 
 the first tight mean-constrained continuity bound 
 on the Shannon entropy of random variables with a 
 countably infinite alphabet. The proof relies on a
  new mean-constrained Fano-type inequality. This c
 lassical result can be used \nto derive a tight en
 ergy-constrained continuity bound for the von\nNeu
 mann entropy.  This is joint work with Simon Becke
 r and Michael Jabbour: IEEE Trans. Inf. Th.\, vol.
  69\, no. 7\, p. 4128-4144 (2023).
LOCATION:MR5\, CMS Pavilion A
CONTACT:Prof. Ramji Venkataramanan
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