  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.
