Already in the case of finite dimensional Hilbert spaces the general form of density matrices ρ is not known. The main reason for this lack of knowledge is the nonlinear constraint for these matrices. We propose a representation of density matrices on finite dimensional Hilbert spaces in terms of finitely many independent parameters. For dimensions 2, 3, and 4 we write down this representation explicitly. As a further application of this representation we study the time dependence of density matrices ρ(t) which in our case is implemented through time dependence of the independent parameters. Under obvious differentiability assumptions the explicit form of is determined. As a special case we recover, for instance, the Lindblad form.
['Erwin Brüning', 'Francesco Petruccione']
Density Matrices and Their Time Evolution