Approximation of quasi-states on manifolds

Adi Dickstein, Frol Zapolsky

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A very interesting and fundamental example is given by the so-called median quasi-state on S2. In this paper we present an algorithm which numerically computes it to any specified accuracy. The error estimate of the algorithm crucially relies on metric continuity properties of a map, which constructs quasi-states from probability measures, with respect to appropriate Wasserstein metrics. We close with non-approximation results, particularly for symplectic quasi-states.

    Original languageEnglish
    Pages (from-to)221-248
    Number of pages28
    JournalJournal of Applied and Computational Topology
    Volume3
    Issue number3
    DOIs
    StatePublished - 9 Sep 2019

    Keywords

    • Computation
    • Quasi-states
    • Reeb graph
    • Symplectic quasi-states
    • Topological measures
    • Wasserstein metrics

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