  The spin-coherent-state positive-operator-valued-measure (POVM) is a
fundamental measurement in quantum science, with applications including
tomography, metrology, teleportation, benchmarking, and measurement of Husimi
phase space probabilities. We prove that this POVM is achieved by collectively
measuring the spin projection of an ensemble of qubits weakly and
isotropically. We apply this in the context of optimal tomography of pure
qubits. We show numerically that through a sequence of weak measurements of
random directions of the collective spin component, sampled discretely or in a
continuous measurement with random controls, one can approach the optimal
bound.
