  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 the 2-sphere. 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.
