  Basing on the analogy between the coherent states of light and separable
states of $N$ bosons, we demonstrate that the violation Cauchy-Schwarz
inequality for any-order correlation function signals the entanglement among
the constituent particles. Rather than restricting to the correlations between
the positions of particles, we consider the broadest set of measurements
allowed by quantum mechanics. Our result is general -- it applies to any
quantum system of bosons, even when the number of particles is not fixed,
provided that there is no coherence between different number states. We also
demonstrate that the compact expression for the separable state of bosons can
be used to relate some known metrological quantities to the particle
entanglement in a very simple way.
