  The entanglement of formation (EOF) is computed for arbitrary two-mode
Gaussian states. Apart from a conjecture, our analysis rests on two main
ingredients. The first is a four-parameter canonical form we develop for the
covariance matrix, one of these parameters acting as a measure of EOF, and the
second is a generalisation of the EPR correlation, used in the work of Giedke
{\em et al} [Phys. Rev. Lett. {\bf 91}, 107901 (2003)], to noncommuting
variables. The conjecture itself is in respect of an extremal property of this
generalized EPR correlation.
