BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Frei (University of Copenhagen) DTSTART:20221012T190000Z DTEND:20221012T200000Z DTSTAMP:20260420T052915Z UID:NYC-NCG/112 DESCRIPTION:Title: Operator algebras and quantum information: Connes implies Tsirelson and robust self-testing\nby Alexander Frei (University of Copenhagen) as part of Noncommutative geometry in NYC\n\n\nAbstract\nWe give a very simpl e proof of Connes implies Tsirelson\,\nand further advertise a hot topic i n quantum information: optimal states and robust self-testing. We showcase here how operator algebraic techniques can be quite fruitful.\n\nFor this we begin with by recalling quantum strategies in the context of non-local games\, and their description in terms of the state space on the full gro up algebra of certain free groups.\n\nWith this description at hand\, we t hen directly obtain the main result via an elementary lifting result by Ki m\, Paulsen and Schafhauser:\nthe Connes embedding problem implies the syn chronous Tsirelson conjecture.\n\nAs such the entire proof is elementary\, \nand bypasses all versions of Kirchberg's QWEP conjecture and the like\,\ nas well as any reformulation such as in terms of the micro state conjectu re.\n\nMoreover\, it should be (likely) easier to construct minimal nonloc al games as counterexamples for the synchronous Tsirelson conjecture (whic h is equivalent to the full Tsirelson conjecture but in a non-trivial way) and so also nonamenable traces for above groups\, in other words non-Conn es embeddable operator algebras.\n\n\n\nAfter this we continue (as much as time permits) with an advertisement for one of the hottest topics in quan tum information:\ndevice-independent certification of quantum states\, or in short ROBUST SELF-TESTING\,\nwhich has tremendous importance for the co ming era of practical quantum computing.\nand we showcase how operator alg ebraic techniques can be quite fruitful here.\n\nMore precisely\, we illus trate these techniques on the following two prominent classes of nonlocal games:\n\n1) The tilted CHSH game.\nWe showcase here how to compute the qu antum value using operator algebraic techniques\, and how to use the same to derive uniqueness for entire optimal states\, including all higher mome nts as opposed to correlations defined on two-moments only\, where the lat ter compares to traditional self-testing.\nMoreover\, we report in this ex ample on previously unknown phase transitions on the uniqueness of optimal states when varying the parameters for the tilted CHSH game.\n\n2) The Me rmin--Peres magic square and magic pentagram game.\nAs before\, we also no te here uniqueness of optimal states\, which in these two examples is a ba sically familiar result.\n\nThe first part is based on preprint: https://a rxiv.org/abs/2209.07940\nThe second part on self-testing (and further robu st self-testing) is based on joint work with Azin Shahiri.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/112/ END:VEVENT END:VCALENDAR