  The trace over the degrees of freedom located in a subset of the space
transforms the vacuum state into a mixed density matrix with non zero entropy.
This is usually called entanglement entropy, and it is known to be divergent in
quantum field theory (QFT). However, it is possible to define a finite quantity
F(A,B) for two given different subsets A and B which measures the degree of
entanglement between their respective degrees of freedom. We show that the
function F(A,B) is severely constrained by the Poincare symmetry and the
mathematical properties of the entropy. In particular, for one component sets
in two dimensional conformal field theories its general form is completely
determined. Moreover, it allows to prove an alternative entropic version of the
c-theorem for 1+1 dimensional QFT. We propose this well defined quantity as the
meaningfull entanglement entropy and comment on possible applications in QFT
and the black hole evaporation problem.
