Relation between entanglement and average number of modes that are taken by constituent particles of coboson

Let we have composite boson made of pair of fermions, and fermions are entangled with each other. The state of composite boson can be written as $$\sum_m \sqrt{\lambda_m} a^{\dagger}_m b^{\dagger}_m |0>$$ where $$\sqrt{\lambda_m}$$ are probability amplitudes that both particles occupy mode $$m$$. We can measure the entanglement between particles is in terms of the amplitude $$\sqrt{\lambda_m}$$. In particular,one can introduce a measure of entanglement known as purity $$P = \sum_m {\lambda_m}^2$$ and $$0 . Then we can find entanglement by using relation $$k=\frac{1}{P}=\frac{1}{{\sum_m \lambda_m}^2}$$. Intuitively, $$K$$ estimates the average number of modes that are taken into account in the internal structure of a composite boson. I am not understanding the relation between entanglement and average number of modes that are taken into account in the internal structure of a composite boson are related? how we can estimate entanglement by knowing average number of modes taken ?