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The separability problem is one of the basic and emergent problems in thepresent and future quantum information processing. The latter focuses oninformation and computing based on quantum mechanics and uses quantum bits asits basic information units. In this paper, we present an overview of theprogress in the separability problem in bipartite systems, more specifically intwo quantum bits systems from the criterion based on the inequalities of Bellin $1964$ to the recent criteria of separability in 2018.

Quantum entanglement: an overview of the separability problem in two quantum bits