TITLE:
Dynamic Violation of Bell’s Inequalities in the Angular Momentum Representation
AUTHORS:
Julio Alberto López-Saldívar, Octavio Castaños, Sergio Cordero, Ramón López-Peña, Eduardo Nahmad-Achar
KEYWORDS:
Density Matrix, Angular Momentum, Bell Inequality, Entanglement
JOURNAL NAME:
Journal of Modern Physics,
Vol.16 No.1,
January
26,
2025
ABSTRACT: A parametrization of density matrices of
d
dimensions in terms of the raising
J
+
and lowering
J
−
angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A general expression for the density matrix of the composite system of angular momenta
j
1
and
j
2
is obtained. In this matrix representation violations of the Bell-Clauser-Horne-Shimony-Holt inequalities are established for the
X
-states of a qubit-qubit, pure and mixed, composite system, as well as for a qubit-qutrit density matrix. In both cases maximal violation of the Bell inequalities can be reached, i.e., the Cirel’son limit. A correlation between the entanglement measure and a strong violation of the Bell factor is also given. For the qubit-qutrit composite system a time-dependent convex combination of the density matrix of the eigenstates of a two-particle Hamiltonian system is used to determine periodic maximal violations of the Bell’s inequality.