This article is cited in 7 papers

Generalized Bell inequality and a method for its verification

V. A. Andreev

P. N. Lebedev Physical Institute, Russian Academy of Sciences

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 $\vec a$, $\vec b$, $\vec c$, 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.

Received: 18.12.2006

DOI: 10.4213/tmf6105

 English version: Theoretical and Mathematical Physics, 2007, 152:3, 1286–1298

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