Criteria for two distinguishable fermions to behave like a boson

TL;DR

This paper investigates the conditions under which a composite of two distinguishable fermions can mimic bosonic behavior, challenging the idea that high entanglement alone guarantees such bosonic properties.

Contribution

It provides a detailed analysis using quantum information tools to clarify the role of entanglement in boson-like behavior and presents counterexamples to previous hypotheses.

Findings

High entanglement does not always lead to bosonic behavior.

The role of entanglement in bosonic properties is more nuanced than previously thought.

Counterexamples show that entanglement alone is insufficient for bosonic characteristics.

Abstract

We study the necessary conditions for bosons composed of two distinguishable fermions to exhibit bosonic-like behaviour. We base our analysis on tools of quantum information theory such as entanglement and the majorization criterion for probability distributions. In particular we scrutinize a recent interesting hypothesis by C. K. Law in the Ref. Phys. Rev. A 71, 034306 (2005) that suggests that the amount of entanglement between the constituent fermions is related to the bosonic properties of the composite boson. We show that a large amount of entanglement does not necessarily imply a good boson-like behaviour by constructing an explicit counterexample. Moreover, we identify more precisely the role entanglement may play in this situation.