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

POVM construction: a simple recipe with applications to symmetric states