  We describe inflation in terms of a time dependent quantum density matrix
with time playing the role of a stochastic variable. Using a quasi-de Sitter
model we compute the corresponding quantum Fisher information function as the
second derivative of the relative entanglement entropy for the density matrix
at two different times. Employing standard quantum estimation theory we
evaluate the minimal variance of quantum scalar fluctuations that reproduces
the power spectrum and the corresponding tilt in the slow roll limit. The
Jeffreys prior associated with such Fisher information can be used to define
the probabilities on the set of initial conditions defined by the slow roll
parameter $\epsilon$ and the initial Shannon information.
