On the separability problem for quantum composite systems

The present article addresses the so-called “quantum separability problem”, the mathematical issue that lies in foundations of quantum information and communication theory. The separability problem consist in elaboration of efficient computational algorithms for determination of whether a given state of a composite quantum system admits representation in a product form, with factors corresponding to each subsystem. The measurement theoretical aspects of this problem are discussed and the geometric probability of the mixed separable/entangled states in quantum systems composed from 2-qubits and qubit-qutrit pairs are computed.