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DTSTART;TZID=Europe/Berlin:20261021T161500
DTEND;TZID=Europe/Berlin:20261021T161500
DTSTAMP:20261031T165754
CREATED:20261015T162438Z
LAST-MODIFIED:20261015T162448Z
UID:10000162-1792599300-1792599300@www.trr352.de
SUMMARY:Regularity of Quantum Trajectories and Randomized Measurements
DESCRIPTION:Quantum trajectories are Markov chains that model the evolution of quantum systems subjected to repeated indirect measurements. The classification of their invariant measures relies heavily on a purification assumption that\, while standard\, is difficult to check for a given instrument. Moreover\, little is known about the invariant measures themselves\, like their support or continuity properties.\nWith Sascha Lill and Cornelia Vogel we recently investigated these questions when the measurements are randomized. Namely\, at each time step\, the observable measured on the probe used for the indirect measurement is chosen randomly and independently. Considering this randomization\, we give sufficient conditions for purification to hold\, the invariant measure’s support is the full set of pure states and the invariant measure is absolutely continuous with respect to the uniform measure. Along the way we introduce a new notion of irreducibility for quantum channels we dub multiplicative primitiveness. We provide examples where it holds and some where it does not. That especially shows that\, for some quantum channels\, whatever the measurement used on the probes\, some pure states will never be approximated by the quantum trajectory.\nI will present these results and related open questions.
URL:https://www.trr352.de/event/regularity-of-quantum-trajectories-and-randomized-measurements/
LOCATION:A027\, Theresienstr. 37\, Munich\, Germany
CATEGORIES:Talks
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DTSTART;TZID=Europe/Berlin:20261030T143000
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DTSTAMP:20261031T165754
CREATED:20261028T141754Z
LAST-MODIFIED:20261028T141903Z
UID:10000164-1793370600-1793385000@www.trr352.de
SUMMARY:Probability Colloquium Augsburg-Munich
DESCRIPTION:Speakers: \n\nAmol Aggarwal (Stanford)\nJohannes Alt (Bonn)\n\nSchedule: \n\n14:30   Welcome\n15:00   Talk Amol Aggarwal\n16:00   Refreshment break\n16:30   Talk Johannes Alt\n18:30   Option for common dinner\n \nTitles and abstracts: \nAmol Aggarwal: Asymptotics for the Maximal Representation of the Symmetric Group \nWe analyze the behavior of the largest dimension of an irreducible representation of the symmetric group S_N\, as N tends to infinity\, showing that it behaves as (N!)^{1/2} * e^{-(d+o(1)) N^{1/2}}\, for some constant d>0. The proof is based on viewing these dimensions as discrete variants of random matrix integrals or Coulomb gases\, and setting up and analyzing a variational principle for their local statistics. \nJohannes Alt: Random Graphs: From Spectra to Quantum Dynamics \nWe study the Erdős-Rényi graph\, a common random graph model with intricate behaviours. \nFirst\, I establish a transition in the eigenvector structure of its adjacency matrix. For large enough expected degree\, all eigenvectors are delocalized\, i.e. their mass spreads out approximately uniformly over all vertices. When the expected degree is small enough\, localized eigenvectors emerge. More precisely\, the mass of each eigenvector with large eigenvalue is concentrated in a ball around a unique vertex and decays exponentially in the graph distance from this vertex. \nSecond\, I determine the Schrödinger time evolution of a free quantum particle hopping on the Erdős-Rényi graph through refined spectral information. \nThird\, I demonstrate that for the corresponding directed Erdős-Rényi graph\, all eigenvectors\, with eigenvalue away from zero\, are delocalized. This is in contrast to the undirected setting in the first part. \nThe talk is based on joint works with Raphael Ducatez\, Antti Knowles and Sarah Timhadjelt.
URL:https://www.trr352.de/event/probability-colloquium-augsburg-munich-3/
LOCATION:University of Augsburg\, Room 2004 (L1)\, Universitätsstraße 14\, Augsburg\, 86159
CATEGORIES:Talks
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