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SUMMARY:From Classical to Quantum: Uniform Continuity Bounds on Entropies 
 in Infinite Dimensions - Prof. Nilanjana Datta\, DAMTP
DTSTART:20241127T140000Z
DTEND:20241127T150000Z
UID:TALK222169@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:  It is known that the Shannon entropy is discontinuous for di
 screte random variables with a countably infinite alphabet. Analogously\, 
 in the quantum case\, the von Neumann entropy is discontinuous for quantum
  states on an infinite-dimensional\, separable Hilbert space. However\, co
 ntinuity can be restored by imposing natural constraints on the random var
 iables (resp. quantum states).  We obtain the first tight mean-constrained
  continuity bound on the Shannon entropy of random variables with a counta
 bly infinite alphabet. The proof relies on a new mean-constrained Fano-typ
 e inequality. This classical result can be used \nto derive a tight energy
 -constrained continuity bound for the von\nNeumann entropy.  This is joint
  work with Simon Becker and Michael Jabbour: IEEE Trans. Inf. Th.\, vol. 6
 9\, no. 7\, p. 4128-4144 (2023).
LOCATION:MR5\, CMS Pavilion A
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