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.
Bibliographical noteFunding Information:
A. D. is partially supported by the Israel Science Foundation Grant 1380/13. F. Z. is partially supported by the Israel Science Foundation Grant 1825/14, and by Grant Number 1281 from the GIF, the German–Israeli Foundation for Scientific Research and Development.
© 2019, Springer Nature Switzerland AG.
- Reeb graph
- Symplectic quasi-states
- Topological measures
- Wasserstein metrics
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Geometry and Topology