  We propose a simple method for constructing POVMs using any set of matrices
which form an orthonormal basis for the space of complex matrices. Considering
the orthonormal set of irreducible spherical tensors, we examine the properties
of the construction on the $N+1$-dimensional subspace of the $2^N$-dimensional
Hilbert space of $N$ qubits comprising the permutationally symmetric states.
Similar in spirit to Neumark's result on realization of a POVM as a projective
measurement, we present a method to physically realize the constructed POVMs
for symmetric states using the Clebsch--Gordan decomposition of the tensor
product of irreducible representations of the rotation group. We illustrate the
proposed construction on a spin-1 system, and show that it is possible to
generate entangled states from separable ones.
