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**1. Homework Statement**

Consider an ensemble of spin 1 systems (a mixed state made of the spin 1 system). The density matrix is now a 3x3 matrix. How many independent parameters are needed to characterize the density matrix? What must we know in addition to S

_{x}, S

_{y}and S

_{z}to characterize the mixed state completely?

**2. The attempt at a solution**

I know that 8 parameters are needed to characterize the density matrix (9 elements, minus one because we know the trace of the density matrix is one.) However, I'm not sure what else is needed to characterize it... S

_{x}, S

_{y}and S

_{z}are all that is needed for the spin 1/2 state, which is all that is treated in all of the books in which I've found a treatment of the density matrix (Sakurai, Gottfried/Yan, Shankar).

When I Google the problem, I get a nonsensical solution that suggests things to do with polarization and quadripole moments, but no explanation of the answer.