## 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 S^{2}. 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 language | English |
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Pages (from-to) | 221-248 |

Number of pages | 28 |

Journal | Journal of Applied and Computational Topology |

Volume | 3 |

Issue number | 3 |

DOIs | |

State | Published - 9 Sep 2019 |

### Bibliographical note

Funding 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.

Publisher Copyright:

© 2019, Springer Nature Switzerland AG.

## Keywords

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

## ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Geometry and Topology