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SUMMARY:Quantum information measures for restricted sets of observables
DTSTART;VALUE=DATE-TIME:20180419T060000Z
DTEND;VALUE=DATE-TIME:20180419T070000Z
DTSTAMP;VALUE=DATE-TIME:20190122T162615Z
UID:indico-event-6384@cern.ch
DESCRIPTION:We study measures of quantum information when the space spanne
d by the set of accessible observables is not closed under products\, i.e.
\, we consider systems where an observer may be able to measure the expect
ation values of two operators\, O_1 and O_2\, but may not have access to O
_1 O_2. This problem is relevant for the study of localized quantum inform
ation in gravity since the set of approximately-local operators in a regio
n may not be closed under arbitrary products. While we cannot naturally as
sociate a density matrix with a state in this setting\, it is still possib
le to define a modular operator for a state\, and distinguish between two
states using a relative modular operator. These operators are defined on a
little Hilbert space\, which parameterizes small deformations of the syst
em away from its original state\, and they do not depend on the structure
of the full Hilbert space of the theory. We extract a class of relative-en
tropy-like quantities from the spectrum of these operators that measure th
e distance between states\, are monotonic under contractions of the set of
available observables\, and vanish only when the states are equal. Conseq
uently\, these distance-measures can be used to define measures of biparti
te and multipartite entanglement. We describe applications of our measures
to coarse-grained and fine-grained subregion dualities in AdS/CFT and pro
vide a few sample calculations to illustrate our formalism.\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=6384
LOCATION: A 304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6384
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