Table 1 Quantum violations of the inequality (4) with C given by (9)

From: Disproving hidden variable models with spin magnitude conservation

s

β and \(\bar \beta\)

s(s + 1)

1

\(- 1 - \frac{1}{{\sqrt 2 }} \approx - 1.707\)

−2

\(- 1 - \sqrt 2 \approx - 2.414\)

 

2

\(- 1 + \frac{1}{{\sqrt 2 }} - 4\sqrt 2 \approx - 5.949\)

−6

\(- 4 - 4\sqrt 2 \approx - 9.657\)

 

3

\(- 4(1 + \sqrt 2 ) \approx - 9.657\)

−12

\(- 9 - 9\sqrt 2 \approx - 21.730\)

 

4

\(- 14\sqrt 2 \approx - 19.799\)

−20

\(- 16 - 16\sqrt 2 \approx - 38.627\)

 
  1. β denotes the classical HV bound taking into account the conservation of the spin vector magnitude, whereas \(\bar \beta\) denotes the HV bound without that additional constraint