1. All-versus-nothing proof of Bell’s theorem for two observers

2. Part I: Proofs of Bell’s theorem “without inequalities” (for qubits)
Part I: Proofs of Bell’s theorem “without inequalities” (for qubits). Beating EPR using their own weapons (perfect correlations)

3. (Mermin’s version of) Greenberger, Horne and Zelinger’s proof

4. Hardy’s proof
Any pure two-qubit entangled, but not maximally entangled, state (Hardy state) can be written as
Logical argument:
Therefore,
“A veces” = “Sometimes”
“Siempre” = “Always”
“Nunca” = “Never”

8. FAQ
What if the measurement of x1x2 changes v(z1z2)?
Do you need to assume that v(z1z2) does not change when Alice measures the compatible observable x1x2?
Do you need to assume noncontextuality in addition to EPR’s elements of reality?
No. The assumption of EPR's elements of reality prevents that v(z1z2) changes when x1x2 is measured on Alice's subsystem (qubits 1 and 2).
The key is to note that v(z1z2) can be predicted with certainty from space-like separated measurements on Bob's subsystem (qubits 3 and 4).
Bob's prediction for v(z1z2) is always confirmed: not only when z1z2 is measured alone, but also when z1z2 and x1x2 are measured together, and when z1z2 is measured after x1x2.

9. The beauty contest

10. The beauty contest

11. The beauty contest

12. Part II: Experimental all-versus-nothing proof of Bell’s theorem for two observers