Scenario

[(3 2) (2 2 2)]

Description

Local facet in [(3 2) (2 2 2)], solved by SymPol.

Cross references

#3

Bell expression and bounds

$$ \left (\begin{array}{rr:rr:rr} \tooltip{0}{P(11|11)} & \tooltip{0}{P(21|11)} & \tooltip{0}{P(31|11)} & \tooltip{0}{P(11|21)} & \tooltip{0}{P(21|21)} \\ \tooltip{0}{P(12|11)} & \tooltip{0}{P(22|11)} & \tooltip{0}{P(32|11)} & \tooltip{0}{P(12|21)} & \tooltip{0}{P(22|21)} \\ \tooltip{- \frac{5}{12}}{P(11|12)} & \tooltip{\frac{7}{12}}{P(21|12)} & \tooltip{- \frac{5}{12}}{P(31|12)} & \tooltip{- \frac{7}{12}}{P(11|22)} & \tooltip{\frac{5}{12}}{P(21|22)} \\ \hdashline \tooltip{\frac{5}{12}}{P(12|12)} & \tooltip{- \frac{7}{12}}{P(22|12)} & \tooltip{\frac{5}{12}}{P(32|12)} & \tooltip{\frac{7}{12}}{P(12|22)} & \tooltip{- \frac{5}{12}}{P(22|22)} \\ \tooltip{\frac{5}{12}}{P(11|13)} & \tooltip{- \frac{7}{12}}{P(21|13)} & \tooltip{\frac{5}{12}}{P(31|13)} & \tooltip{- \frac{5}{12}}{P(11|23)} & \tooltip{\frac{7}{12}}{P(21|23)} \\ \tooltip{- \frac{5}{12}}{P(12|13)} & \tooltip{\frac{7}{12}}{P(22|13)} & \tooltip{- \frac{5}{12}}{P(32|13)} & \tooltip{\frac{5}{12}}{P(12|23)} & \tooltip{- \frac{7}{12}}{P(22|23)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|r:r:r} \tooltip{-1}{P_(|)} & \tooltip{0}{P_A(1|1)} & \tooltip{0}{P_A(2|1)} & \tooltip{2}{P_A(1|2)} \\ \hline \tooltip{0}{P_B(1|1)} & \tooltip{0}{P_AB(1,1|1,1)} & \tooltip{0}{P_AB(2,1|1,1)} & \tooltip{0}{P_AB(1,1|2,1)} \\ \tooltip{0}{P_B(1|2)} & \tooltip{0}{P_AB(1,1|1,2)} & \tooltip{2}{P_AB(2,1|1,2)} & \tooltip{-2}{P_AB(1,1|2,2)} \\ \hdashline \tooltip{2}{P_B(1|3)} & \tooltip{0}{P_AB(1,1|1,3)} & \tooltip{-2}{P_AB(2,1|1,3)} & \tooltip{-2}{P_AB(1,1|2,3)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } \frac{5}{12} \text{ } P(11|12) \text{ } \text{+} \text{ } \frac{7}{12} \text{ } P(21|12) \text{ } \text{-} \text{ } \frac{5}{12} \text{ } P(31|12) \text{ } \text{-} \text{ } \frac{7}{12} \text{ } P(11|22) \\ \frac{5}{12} \text{ } P(21|22) \text{ } \text{+} \text{ } \frac{5}{12} \text{ } P(12|12) \text{ } \text{-} \text{ } \frac{7}{12} \text{ } P(22|12) \text{ } \text{+} \text{ } \frac{5}{12} \text{ } P(32|12) \\ \frac{7}{12} \text{ } P(12|22) \text{ } \text{-} \text{ } \frac{5}{12} \text{ } P(22|22) \text{ } \text{+} \text{ } \frac{5}{12} \text{ } P(11|13) \text{ } \text{-} \text{ } \frac{7}{12} \text{ } P(21|13) \\ \frac{5}{12} \text{ } P(31|13) \text{ } \text{-} \text{ } \frac{5}{12} \text{ } P(11|23) \text{ } \text{+} \text{ } \frac{7}{12} \text{ } P(21|23) \text{ } \text{-} \text{ } \frac{5}{12} \text{ } P(12|13) \\ \frac{7}{12} \text{ } P(22|13) \text{ } \text{-} \text{ } \frac{5}{12} \text{ } P(32|13) \text{ } \text{+} \text{ } \frac{5}{12} \text{ } P(12|23) \text{ } \text{-} \text{ } \frac{7}{12} \text{ } P(22|23)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } 1 \text{ } P_(|) \text{ } \text{+} \text{ } 2 \text{ } P_A(1|2) \text{ } \text{+} \text{ } 2 \text{ } P_AB(2,1|1,2) \text{ } \text{-} \text{ } 2 \text{ } P_AB(1,1|2,2) \\ 2 \text{ } P_B(1|3) \text{ } \text{-} \text{ } 2 \text{ } P_AB(2,1|1,3) \text{ } \text{-} \text{ } 2 \text{ } P_AB(1,1|2,3)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$

Symmetry group

Symmetry group of order: 8

Generators:

  • liftings :
    • B1(1,2)
    • A1(1,3)
  • outputInputPerms :
    • A2(1,2) B2(1,2) B3(1,2) B(2,3)

Extras