  We show that it is possible to reach the sub shot-noise sensitivity of the
phase estimation using two independently prepared Bose-Einstein condensates as
an input of an interferometer. In this scenario, the quantum correlations
between the particles, which are necessary to beat the shot-noise limit, arise
from the indistinguishability of bosons. Allowing for atom number fluctuations
independently in each condensate, we calculate the ultimate bound of the
sensitivity. Our main conclusion is that even in presence of major atom number
fluctuations, an interferometer operating on two independent condensates can
give very high sensitivity. We also show that the estimation from the
measurement of the number of atoms utilizes these quantum correlations. This
observation, in context of recent measurement of the Fisher information in a
many-body system [H. Strobel {\it et al}, Science {\bf 345}, 424 (2014)], opens
the way towards the construction of a new type of an interferometer operating
below the shot-noise limit.
