Geodesic
Generalized Bell inequality and a~method for its verification
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 488-501

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We use the reduced density matrix of the two-particle spin state to construct a generalized Bell–Clauser–Horne–Shimony–Holt inequality. For each specific state and under a special choice of the vectors $\vec a$, $\vec b$, $\vec c$, and $\vec d$, this inequality becomes an exact equality. We show how such vectors can be found using the reduced density matrix. Both sides of this equality have a specific numerical value. We indicate the connection of this number with the measure of entanglement of the two-particle spin state.
Keywords: quantum mechanics, entangled state, density matrix, Bell inequality. 
@article{TMF_2007_152_3_a6,
     author = {V. A. Andreev},
     title = {Generalized {Bell} inequality and a~method for its verification},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {488--501},
     publisher = {mathdoc},
     volume = {152},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a6/}
}
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V. A. Andreev. Generalized Bell inequality and a~method for its verification. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 3, pp. 488-501. http://geodesic.mathdoc.fr/item/TMF_2007_152_3_a6/