  A new conceptual key generation scheme is presented by using intrinsic
quantum correlations of single photons between Alice and Bob. The intrinsic
bi-partite correlation functions allow key bit to be generated through high
level communication language i.e. a key bit is directly encoded to shared
correlation functions not to the state and detection of a photon at Bob does
not mean key bit. These make the scheme robust against intercept-resend attack
because Alice and Bob can always check the errors in their measurements and
reveal the presence of Eve in their channel without leaking any key bit
information. The laser source is located in the middle of Alice and Bob,
consists of two modes (x,y), relatively random phase-modulated $(\pm
\frac{\pi}{2})$ weak coherent states combined in a perfect 50/50 beam splitter.
The scheme is strictly relied on the perfect beam splitter and mean photon
number less than 1, where more than one photon in a coherent pulse will
introduce more errors in Bob even without the presence of Eve. From the
percentage of errors in Bob, we can estimate the amount of information will be
leaked to Eve in the photon-number splitting attack. This scheme can preserve
the randomness of phase-randomized light source for doubling the communication
distance as in original Ekert's protocol and providing the raw key generation
rate a factor of 2 higher than weak coherent light protocols.
