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DTSTAMP:20260424T143216Z
UID:64b9491b15a4d850665576@ist.ac.at
DTSTART:20240326T161500
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DESCRIPTION:Speaker: Cornelia Vogel\nhosted by Laszlo Erdös\nAbstract: We 
 generalize Lévy's Lemma\, a concentration-of-measure result for the unifo
 rm probability distribution on high-dimensional spheres\, to a more genera
 l class of measures\, so-called GAP measures. For any given density matrix
  rho on a separable Hilbert space H\, GAP(rho) is the most spread out prob
 ability measure on the unit sphere of H that has density matrix rho and th
 us forms the natural generalization of the uniform distribution. We prove 
 concentration-of-measure whenever the largest eigenvalue ||rho|| of rho is
  small. With the help of this result we generalize the well-known and impo
 rtant phenomenon of ''canonical typicality'' to GAP measures. Canonical ty
 picality is the statement that for ''most'' pure states psi of a given ens
 emble\, the reduced density matrix of a sufficiently small subsystem is ve
 ry close to a psi-independent matrix. So far\, canonical typicality is kno
 wn for the uniform distribution on finite-dimensional spheres\, correspond
 ing to the micro-canonical ensemble. Our result shows that canonical typic
 ality holds in general for systems described by a density matrix with smal
 l eigenvalues. Since certain GAP measures are quantum analogs of the canon
 ical ensemble of classical mechanics\, our results can also be regarded as
  a version of equivalence of ensembles. The talk is based on joint work wi
 th Stefan Teufel and Roderich Tumulka.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Cornelia Vogel: Concentration of measure for thermal distributions 
 of quantum states
URL:https://talks-calendar.ista.ac.at/events/4866
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