  It is well established that unpolarized light is invariant with respect to
any SU(2) polarization transformation. This requirement fully characterizes the
set of density matrices representing unpolarized states. We introduce the
degree of polarization of a quantum state as its distance to the set of
unpolarized states. We use two different candidates of distance, namely the
Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally
different degrees of polarization. We apply these notions to relevant field
states and we demonstrate that they avoid some of the problems arising with the
classical definition.
