BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cambyze Rouze (U. München) DTSTART:20210618T141500Z DTEND:20210618T150000Z DTSTAMP:20260423T035409Z UID:OpenPDEA/11 DESCRIPTION:Title: (Seminar) Quantum modified logarithmic Sobolev inequalities\nby Camb yze Rouze (U. München) as part of Open PDE and analysis seminar and lectu res\n\n\nAbstract\nFunctional inequalities constitute by now a well-establ ished \ntheory with many connections to other fields of mathematics such a s \nconcentration of measure\, mixing times of Markov processes or optimal \ntransport to name only a few. Among these inequalities\, the modified \nlogarithmic Sobolev inequality (MLSI) controls the exponential entropic \nconvergence of a Markov semigroup towards its stationary measure. \nAlth ough introduced almost simultaneously\, their quantum analogues have \nlon g suffered from the loss of certain key properties inherent to the \npassa ge to the non-commutative realm. Perhaps the most important of \nthese is the tensorization property\, which often allows one to prove a \nfunctiona l inequality for a Markov process on an uncountable state space \nby reduc tion to the two-points space.\nDue to the absence of generic tensorization results for the MLSI in the \nquantum setting\, one is often forced to pr ove it case by case. However\, \nin the recent years\, a new approach to t he problem emerged from the \ncommunities of operator algebras and quantum information theory. Here\, \ninstead of proving the tensorization of MLSI for a product of \nsemigroups\, one considers a stronger inequality which naturally \ntensorizes\, namely the complete modified logarithmic Sobolev inequality \n(CMLSI). The latter consists in proving the inequality for t he semigroup \ntensorized with the identity semigroup over an arbitrarily large matrix \nalgebra. The existence of CMLSI for all quantum Markov semi groups on \nmatrix algebras was however left as an open conjecture.\nIn th is talk\, I will provide a proof of the conjecture for the class of \nreve rsible quantum Markov semigroups. This talk is intended to be \nself-conta ined and does not require previous knowledge about quantum \nmechanics or quantum information theory. It is based on a joint work \nwith Li Gao\, a preprint of which is available here: \nhttps://arxiv.org/abs/2102.04146.\n LOCATION:https://researchseminars.org/talk/OpenPDEA/11/ END:VEVENT END:VCALENDAR