Classical limit of entangled states of two angular momenta

M. Kuś, J. Mostowski, J. Pietraszewicz

Published 2018-11-26Version 1

We consider the classical limit of a system of two particles, each with arbitrary angular momentum j, in a state with zero total angular momentum. The state is maximally entangled and therefore exhibits non-classical features. To compare the quantum system with its classical counterpart the probabilities of finding projections of the angular momenta on selected axes are determined. Quantum probabilities are typically used for the study of generalized Bell's inequalities. Violation of these inequalities is a proof that the system differs significantly from a classical probabilistic system with hidden variables. We use statistical methods to show that in the case of very large $j$, most of Bell's inequalities are not violated. Further, it is almost impossible to find an inequality that is violated. In practice, the quantum system cannot be distinguished from its classical counterpart.