CHSH inequality

In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden variable theories. Experimental verification of violation of the inequalities is seen as experimental confirmation that nature cannot be described by local hidden variables theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969 (Clauser et al., 1969). They derived the CHSH inequality, which, as with John Bell's original inequality (Bell, 1964), is a constraint on the statistics of 'coincidences' in a Bell test experiment which is necessarily true if there exist underlying local hidden variables (local realism). This constraint can, on the other hand, be infringed by quantum mechanics. | S | ≤ 2 , {displaystyle |S|leq 2,}     (1) S = E ( a , b ) − E ( a , b ′ ) + E ( a ′ , b ) + E ( a ′ , b ′ ) . {displaystyle S=E(a,b)-Eleft(a,b' ight)+Eleft(a',b ight)+Eleft(a',b' ight).}     (2) E = N + + − N + − − N − + + N − − N + + + N + − + N − + + N − − {displaystyle E={frac {N_{++}-N_{+-}-N_{-+}+N_{--}}{N_{++}+N_{+-}+N_{-+}+N_{--}}}}     (3) | A _ | ≤ 1 | B _ | ≤ 1 {displaystyle left|{underline {A}} ight|leq 1quad left|{underline {B}} ight|leq 1}     (4) In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden variable theories. Experimental verification of violation of the inequalities is seen as experimental confirmation that nature cannot be described by local hidden variables theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969 (Clauser et al., 1969). They derived the CHSH inequality, which, as with John Bell's original inequality (Bell, 1964), is a constraint on the statistics of 'coincidences' in a Bell test experiment which is necessarily true if there exist underlying local hidden variables (local realism). This constraint can, on the other hand, be infringed by quantum mechanics.