Figure 1
Left: Illustration of the POVM
in Eq. (
3) as an example of finitely supported POVM
in Eq. (
6). In this specific example, the outcome space
is the unit sphere
, the dimension of the Hilbert space is
, and only two out of the four terms in Eq. (
6) are nonvanishing:
,
,
. The probability of finding the spin direction in a region
is zero for
missing the two poles, as B in the figure, and is possibly nonzero for
as A. Right: Another example of a finitely supported POVM for
, corresponding to a symmetric informationally complete POVM [
20]. The POVM is made of four elements
corresponding to
at the vertices of a tetrahedron. The probability can be nonvanishing only if the region
contains at least one of these four points, such as in A, whereas it is always zero in situations as in B.
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