Bell’s inequalities that
all local realistic theories obey
and quantum theory can violate
â b̂
2  ha1b1i + ha1b2i + ha2b1i ha2b2i  2
Bell, Physics 1, 195 (1965); CHSH, PRL 23, 880 (1969)

Quantum theory can
violate Bell’s inequality
hâb̂i ⌘ h |âb̂| i
= cos ✓(~
a,~
b)
hB̂i = hâ1b̂1i + hâ1b̂2i + hâ2b̂1i hâ2b̂2i
~
a1
~
a2
~
b1
~
b2
hB̂i =
1
p
2
+
1
p
2
+
1
p
2
✓
1
p
2
◆
= 2
p
2 > 2