TY - JOUR

T1 - Approximation of quasi-states on manifolds

AU - Dickstein, Adi

AU - Zapolsky, Frol

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019/9/9

Y1 - 2019/9/9

N2 - 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.

AB - 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.

KW - Computation

KW - Quasi-states

KW - Reeb graph

KW - Symplectic quasi-states

KW - Topological measures

KW - Wasserstein metrics

UR - http://www.scopus.com/inward/record.url?scp=85105132206&partnerID=8YFLogxK

U2 - 10.1007/s41468-019-00030-1

DO - 10.1007/s41468-019-00030-1

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AN - SCOPUS:85105132206

SN - 2367-1726

VL - 3

SP - 221

EP - 248

JO - Journal of Applied and Computational Topology

JF - Journal of Applied and Computational Topology

IS - 3

ER -