Abstract
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 % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qeguuDJXwAKbacfiGaf8xyaeMbaSaacaGGSaacbaGaa4hiaiqb-jga% Izaalaaaaa!3EC2! $$\vec a, \vec b$$ , 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.
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