Scenario

[(2 2) (2 2)]

Description

CGLMP2/CGLMP, 2002, inequality for 2 outcomes

Cross references

#3

Bell expression and bounds

$$ \left (\begin{array}{rr:rr} \tooltip{1}{P(11|11)} & \tooltip{-1}{P(21|11)} & \tooltip{-1}{P(11|21)} & \tooltip{1}{P(21|21)} \\ \tooltip{-1}{P(12|11)} & \tooltip{1}{P(22|11)} & \tooltip{1}{P(12|21)} & \tooltip{-1}{P(22|21)} \\ \hdashline \tooltip{1}{P(11|12)} & \tooltip{-1}{P(21|12)} & \tooltip{1}{P(11|22)} & \tooltip{-1}{P(21|22)} \\ \tooltip{-1}{P(12|12)} & \tooltip{1}{P(22|12)} & \tooltip{-1}{P(12|22)} & \tooltip{1}{P(22|22)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 2\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} 1 \text{ } P(11|11) \text{ } \text{-} \text{ } 1 \text{ } P(21|11) \text{ } \text{-} \text{ } 1 \text{ } P(11|21) \text{ } \text{+} \text{ } 1 \text{ } P(21|21) \\ \text{-} \text{ } 1 \text{ } P(12|11) \text{ } \text{+} \text{ } 1 \text{ } P(22|11) \text{ } \text{+} \text{ } 1 \text{ } P(12|21) \text{ } \text{-} \text{ } 1 \text{ } P(22|21) \\ 1 \text{ } P(11|12) \text{ } \text{-} \text{ } 1 \text{ } P(21|12) \text{ } \text{+} \text{ } 1 \text{ } P(11|22) \text{ } \text{-} \text{ } 1 \text{ } P(21|22) \\ \text{-} \text{ } 1 \text{ } P(12|12) \text{ } \text{+} \text{ } 1 \text{ } P(22|12) \text{ } \text{-} \text{ } 1 \text{ } P(12|22) \text{ } \text{+} \text{ } 1 \text{ } P(22|22)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 2\text{ (facet)}\end{array} \right. $$

Symmetry group

Symmetry group of order: 16

Generators:

  • outputPerms :
    • A1(1,2) A2(1,2) B1(1,2) B2(1,2)
  • outputInputPerms :
    • A2(1,2) B(1,2)
    • B1(1,2) A(1,2)
  • rest :
    • A(1,2) B(1,2) (A,B)

Extras

Sources