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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 $0 <P<1$. 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 ?

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