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DTSTART:20170326T030000
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DTSTAMP:20260428T235041Z
UID:588f4a7f8f47c438365479@ist.ac.at
DTSTART:20170206T110000
DTEND:20170206T130000
DESCRIPTION:Speaker: Miguel Navascues\nhosted by Mikhail Lemeshko\nAbstract
 : We consider the problem of certifying entanglement and nonlocality in on
 e-dimensional TI infinite systems when just averaged near-neighbor correla
 tors are available. Exploiting the triviality of the marginal problem for 
 1D TI distributions\, we arrive at a practical characterization of the nea
 r-neighbor density matrices of multi-separable TI quantum states. This all
 ows us\, e.g.\, to identify a family of separable two-qubit states which o
 nly admit entangled TI extensions. For nonlocality detection\, we show tha
 t\, when viewed as a vector in R^n\, the set of boxes admitting a TI class
 ical extension forms a polytope\, i.e.\, a convex set defined by a finite 
 number of linear inequalities. We prove that some of these inequalities ca
 n be violated by distant parties conducting identical measurements on an i
 nfinite TI quantum state.\n\nOur attempts at generalizing our results to T
 I systems in 2D and 3D lead us to the (to our knowledge\, virtually unexpl
 ored) problem of characterizing the marginal distributions of infinite TI 
 systems in higher dimensions. In this regard\, we show that\, for random v
 ariables which can only take a small number of possible values (namely\, b
 its and trits)\, the set of nearest (and next-to-nearest) neighbor distrib
 utions admitting a 2D TI infinite extension forms a polytope. This allows 
 us to compute exactly the ground state energy per site of any classical ne
 arest-neighbor Ising-type TI Hamiltonian in the infinite square or triangu
 lar lattice. Remarkably\, some of these results also hold in 3D.\nIn contr
 ast\, when the cardinality of the set of possible values grows (but remain
 s finite)\, we show that the marginal nearest-neighbor distributions of 2D
  TI systems are not described by a polytope or even a semi-algebraic set. 
 Moreover\, the problem of computing the exact ground state energy per site
  of arbitrary 2D TI Hamiltonians is undecidable.\n
LOCATION:Seminar room Big Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Miguel Navascues: Random variables\, entanglement and nonlocality i
 n infinite TI systems
URL:https://talks-calendar.ista.ac.at/events/289
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