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SUMMARY:Nicholas LaRacuente (University of Chicago)
DTSTART:20210118T173000Z
DTEND:20210118T184500Z
DTSTAMP:20260423T024552Z
UID:HET/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HET/12/">Mul
 tivariate Trace Inequalities\, p-Fidelity\, and Universal Recovery Beyond 
 Tracial von Neumann Algebras</a>\nby Nicholas LaRacuente (University of Ch
 icago) as part of Purdue HET\n\n\nAbstract\nTrace inequalities are powerfu
 l in quantum information theory\, often replacing classical functional cal
 culus in noncommutative settings. The physics of quantum field theory and 
 holography\, however\, motivate entropy inequalities in von Neumann algebr
 as that lack a useful notion of a trace. The Haagerup and Kosaki Lp spaces
  enable re-expressing trace inequalities in non-tracial von Neumann algebr
 as. In particular\, we show this for the generalized Araki-Lieb-Thirring a
 nd Golden-Thompson inequalities from (Sutter\, Berta & Tomamichel 2017). T
 hen\, using the Haagerup approximation method\, we prove a general von Neu
 mann algebra version of the recovery map tightening of the data processing
  inequality for relative entropy. We also generalize via subharmonicity of
  a logarithmic p-fidelity of recovery. Furthermore\, we prove that non-dec
 rease of relative entropy is equivalent to existence of an L1-isometry imp
 lementing the channel on both input states.\n
LOCATION:https://researchseminars.org/talk/HET/12/
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