Entanglement and Composite Bosons

We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity that governs the bosonic character of a pair of fermions when N such pairs approximately share the same wavefunction. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity in question approaches its ideal bosonic value.