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DTSTART;TZID=Europe/Paris:20240116T140000
DTEND;TZID=Europe/Paris:20240116T153000
DTSTAMP:20260421T161118
CREATED:20240112T074208Z
LAST-MODIFIED:20240116T090717Z
UID:9436-1705413600-1705419000@fermi.univ-tlse3.fr
SUMMARY:Resserrement des limites de continuité sur les entropies et des limites sur les capacités quantiques. - (Michael Jabbour / LPT / Seminar). - 16/01/2024\, 14 H.
DESCRIPTION:Michael Jabbour  (Université libre de Bruxelles) \nSeminar LPT\, 16/01/2024\, 14H\, 3R1\, seminar room\, 3rd floor \nRésumé: \nOne of the most basic tasks in information theory is communication. The capacity of a quantum channel is the maximum rate at which information can be transmitted through it reliably (in the asymptotic limit) per use of the channel. Mathematically\, the various definitions of capacities are expressed in terms of entropies. They are in general difficult to compute. However\, they can be bounded with the help of continuity bounds on entropies. The latter are generally expressed in terms of a single distance measure between probability distributions or quantum states\, typically\, the total variation- or trace distance. However\, if an additional distance measure is known\, the continuity bounds can be significantly strengthened. Here\, we prove uniform continuity bounds for the Shannon and von Neumann entropies in terms of both the local- and total variation distances for the former\, and both the operator norm- and trace distances for the latter. We then apply our results to compute upper bounds on channel capacities for channels that are ε-close in diamond norm and ν-close in completely bounded spectral norm to their complementary channel when composed with a degrading channel. Moreover\, these bounds can be further improved by considering certain unstabilized versions of the above norms. We show that upper bounds on the latter can be efficiently expressed as semidefinite programs.
URL:https://fermi.univ-tlse3.fr/event/tba-michael-jabbour-lpt-seminar-16-01-2024-14-h/
LOCATION:salle de séminaire 3ème étage\, Bâtiment 3r1 Université Toulouse III\, Toulouse\, 31400\, France
CATEGORIES:Events,LPT,Seminars
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