  Transport through a metallic carbon nanotube is considered, where electrons
are injected in the bulk by a scanning tunneling microscope tip. The charge
current and noise are computed both in the absence and in the presence of one
dimensional Fermi liquid leads. For an infinite homogeneous nanotube, the shot
noise exhibits effective charges different from the electron charge. Noise
correlations between both ends of the nanotube are positive, and occur to
second order only in the tunneling amplitude. The positive correlations are
symptomatic of an entanglement phenomenon between quasiparticles moving right
and left from the tip. This entanglement involves many body states of the boson
operators which describe the collective excitations of the Luttinger liquid.
