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SUMMARY:Belavkin-Staszewski Quantum Markov Chains - Pablo Costa Rico\, Tec
 hincal University of Munich
DTSTART:20250619T131500Z
DTEND:20250619T141500Z
UID:TALK233527@talks.cam.ac.uk
CONTACT:Laurens Lootens
DESCRIPTION:The vanishing of the conditional mutual information (CMI) char
 acterizes quantum Markov chains (QMCs) in the standard setting based on th
 e Umegaki relative entropy. By replacing the Umegaki entropy with the Bela
 vkin-Staszewski (BS) relative entropy\, one can define modified versions o
 f CMIs (called   BS-conditional mutual informations) and refer to quantum 
 states with vanishing BS-CMIs as Belavkin-Staszewski quantum Markov chains
  (BS-QMCs). In this talk\, I will present a framework that establishes a p
 recise relationship between conventional quantum Markov chains and their B
 S counterparts. This framework yields a recovery map for the BS-relative e
 ntropy in the spirtit of the Petz recovery map.  Additionally\, we find a 
 structural decomposition theorem for BS-quantum Markov chains and analyze 
 the behavior of states with approximately vanishing BS-CMI. In addition\, 
 we show that vanishing of the BS-CMIs  does not imply that the marginal in
  the system AC is separable. Thanks to this property we will be able to ge
 nerate BS-QMCs which are QMCs . As an application\, we demonstrate that fo
 r the Gibbs state of a quantum spin chain with finite-range\, translation-
 invariant interactions at positive temperature\, the CMI of some special s
 tates decays superexponentially fast with the size of the intermediate reg
 ion.
LOCATION:Center for Mathematical Sciences\, Lecture room MR2
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