BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mark M. Wilde (Louisiana State University\, USA) DTSTART:20210120T130000Z DTEND:20210120T140000Z DTSTAMP:20260423T052831Z UID:FAOT/4 DESCRIPTION:Title: α- Logarithmic negativity\nby Mark M. Wilde (Louisiana State University\, USA) as part of Functional Analysis and Operator Theory Webinar\n\n\nAbst ract\nThe logarithmic negativity of a bipartite quantum state is a widely employed entanglement measure in quantum information theory\, due to the f act that it is easy to compute and serves as an upper bound on distillable entanglement. More recently\, the $\\kappa$-entanglement of a bipartite s tate was shown to be the first entanglement measure that is both easily co mputable and has a precise information-theoretic meaning\, being equal to the exact entanglement cost of a bipartite quantum state when the free ope rations are those that completely preserve the positivity of the partial t ranspose [Wang and Wilde\, Phys. Rev. Lett. 125(4):040502\, July 2020]. \n \nIn this talk\, we discuss a non-trivial link between these two entanglem ent measures\, by showing that they are the extremes of an ordered family of $\\alpha$-logarithmic negativity entanglement measures\, each of which is identified by a parameter $\\alpha\\in[1\,\\infty]$. In this family\, t he original logarithmic negativity is recovered as the smallest with $\\al pha=1$\, and the $\\kappa$-entanglement is recovered as the largest with $ \\alpha=\\infty$. We prove that the $\\alpha$-logarithmic negativity satis fies the following properties: entanglement monotone\, normalization\, fai thfulness\, and subadditivity. We also prove that it is neither convex nor monogamous. Finally\, we define the $\\alpha$-logarithmic negativity of a quantum channel as a generalization of the notion for quantum states\, an d we show how to generalize many of the concepts to arbitrary resource the ories.\n LOCATION:https://researchseminars.org/talk/FAOT/4/ END:VEVENT END:VCALENDAR