  In a previous paper certain measurable criteria have been derived, that are
sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR)
correlations for measurements with continuous variable outcomes. Here it is
shown how such EPR criteria, which do not demand perfect EPR correlations, can
be used to prove the extent of security for continuous variable quantum
cryptographic schemes (in analogy to that proposed by Ekert) where Alice and
Bob hope to construct a secure sequence of values from measurements performed
on continuous-variable EPR-correlated fields sent from a distant source. It is
proven that the demonstration of the EPR criterion on Alice's and Bob's joint
statistics compels a necessary loss in the ability to infer the results shared
by Alice and Bob, by measurements performed on any third channel potentially
representing an eavesdropper (Eve). This result makes no assumption about the
nature of the quantum source of the fields transmitted to Alice and Bob, except
that the EPR correlations are observed at the final detector locations. In this
way a means is provided to establish security in the presence of some loss and
less than optimal correlation, and against any eavesdropping strategy employed
by Eve prior to detection of the fields by Alice and Bob.
