Entangled states are in conflict with a general physical principle which expresses that a composite entity exists if and only if its components also exist, and the hypothesis that pure states represent the actuality of a physical entity, i.e., its ‘existence’. A possible way to solve this paradox consists in completing the standard formulation of quantum mechanics, by adding more pure states. We show that this can be done, in a consistent way, by using the extended Bloch representation of quantum mechanics, recently introduced to provide a possible solution to the measurement problem. Hence, with the solution proposed by the extended Bloch representation of quantum mechanics, the situation of entangled states regains full intelligibility.

Aerts, D. & Sassoli de Bianchi, M. (2016). A possible solution to the second entanglement paradox. In: Probing the Meaning of Quantum Mechanics. Superpositions, Dynamics, Semantics and Identity, pp. 351-359. Eds. D. Aerts, C. De Ronde, H. Freytes and R. Giuntini, World Scientific Publishing Company, Singapore. Doi: 10.1142/9789813146280_0016.