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DTSTAMP:20261014T204707Z
UID:c157b11a-aded-43d7-bbbc-8aa49215ad57
DTSTART:20261015T140000
DTEND:20261015T153000
DESCRIPTION:How much can the expectation of an observable change when the q
 uantum state is known only approximately? We use a DRO perspective and con
 sider the worst case over a sandwiched Rényi divergence ball of order $\\
 alpha$  around a reference state. Convex duality gives the value in closed
  form in terms of Schatten norms. A classicalization theorem shows that th
 e quantum problem is the classical one for a probability measure on the sp
 ectrum of the observable\, built from Heinävaara's tracial joint spectral
  measure\; for relative entropy\, $\\alpha=1$\, it is the measure of Stahl
 's theorem (the Bessis–Moussa–Villani conjecture). Its variance is sma
 ller than the Born variance whenever state and observable do not commute\,
  which sharpens the classical concentration bounds\, and Pinsker and Fuchs
 –van de Graaf among them\, in the quantum setting.
LOCATION:ETH Zürich\, Hönggerberg HIT E 41.1
ORGANIZER:Luc Rey-Bellet
SUMMARY:Quantum Robustness via Sandwiched Renyi Divergences
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