1301.6500 (Elisa Ercolessi et al.)

Symmetric logarithmic derivative for general n-level systems and quantum
Fisher information tensor for three level systems    [PDF]

Elisa Ercolessi, Michele Schiavina

We give an explicit formula for the computation of the symmetric logarithmic derivative for arbitrarily mixed quantum systems, provided that the structure constants of the associated unitary Lie algebra are known. To give examples of this procedure, we first recover the known formulae for two level mixed and three level pure state systems and then apply it to the novel case of U(3), that is for arbitrarily mixed three level systems (q-trits). Exploiting the latter result, we finally calculate an expression for the Fisher tensor for a threefold mixed q-trit considering also all possible degenerate sub-cases.

View original: http://arxiv.org/abs/1301.6500