Criteria for two distinguishable fermions to form a boson

We study the necessary conditions for systems composed of two distinguishable fermions to exhibit bosonic behavior. We base our analysis on tools of quantum information theory such as entanglement, local operations and classical communication and the majorization criterion for probability distributions. Introduction of these tools yields new insights into the old and important problem of identifying the conditions for existence of composite bosons. We precisely identify the role entanglement plays in the formation and behavior of such composite particles.

Figure 1

The schematic picture presenting the idea of condensation of composite bosons. Each composite boson initially occupies a different potential well. The well energy levels enumerated by $n$ give rise to the internal structure of composite bosons $c^{†}={\sum }_n\sqrt{{\lambda }_n}{a}_n^{†}{b}_n^{†}$. We investigate the possibility of an LOCC operation bringing all composite bosons into one well.