  Self-testing refers to the possibility of characterizing uniquely (up to
local isometries) the state and measurements contained in quantum devices,
based only on the observed input-output statistics. Already in the basic case
of the two-qubit singlet, self-testing is not unique: the two known criteria
(the maximal violation of the CHSH inequality and the Mayers-Yao correlations)
are not equivalent. It is unknown how many criteria there are. In this paper,
we find the whole set of criteria for the ideal self-testing of singlet with
two measurements and two outcomes on each side: it coincides with all the
extremal points of the quantum set that can be obtained by measuring the
singlet.
