Cauchy-Schwarz inequality and particle entanglement

Recently, violation of the Cauchy-Schwarz inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.