Scenario

[(2 2 2) (2 2)]

Description

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

Cross references

#3

Bell expression and bounds

$$ \left (\begin{array}{rr:rr} \tooltip{0}{P(11|11)} & \tooltip{0}{P(21|11)} & \tooltip{- \frac{1}{2}}{P(11|21)} & \tooltip{\frac{1}{2}}{P(21|21)} & \tooltip{- \frac{1}{2}}{P(11|31)} & \tooltip{\frac{1}{2}}{P(21|31)} \\ \tooltip{0}{P(12|11)} & \tooltip{0}{P(22|11)} & \tooltip{\frac{1}{2}}{P(12|21)} & \tooltip{- \frac{1}{2}}{P(22|21)} & \tooltip{\frac{1}{2}}{P(12|31)} & \tooltip{- \frac{1}{2}}{P(22|31)} \\ \hdashline \tooltip{0}{P(11|12)} & \tooltip{0}{P(21|12)} & \tooltip{\frac{1}{2}}{P(11|22)} & \tooltip{- \frac{1}{2}}{P(21|22)} & \tooltip{- \frac{1}{2}}{P(11|32)} & \tooltip{\frac{1}{2}}{P(21|32)} \\ \tooltip{0}{P(12|12)} & \tooltip{0}{P(22|12)} & \tooltip{- \frac{1}{2}}{P(12|22)} & \tooltip{\frac{1}{2}}{P(22|22)} & \tooltip{\frac{1}{2}}{P(12|32)} & \tooltip{- \frac{1}{2}}{P(22|32)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|r:r} \tooltip{-1}{P_(|)} & \tooltip{0}{P_A(1|1)} & \tooltip{0}{P_A(1|2)} & \tooltip{2}{P_A(1|3)} \\ \hline \tooltip{2}{P_B(1|1)} & \tooltip{0}{P_AB(1,1|1,1)} & \tooltip{-2}{P_AB(1,1|2,1)} & \tooltip{-2}{P_AB(1,1|3,1)} \\ \hdashline \tooltip{0}{P_B(1|2)} & \tooltip{0}{P_AB(1,1|1,2)} & \tooltip{2}{P_AB(1,1|2,2)} & \tooltip{-2}{P_AB(1,1|3,2)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|r:r} & \tooltip{0}{<A1>} & \tooltip{0}{<A2>} & \tooltip{0}{<A3>} \\ \hline \tooltip{0}{<B1>} & \tooltip{0}{<A1 B1>} & \tooltip{- \frac{1}{2}}{<A2 B1>} & \tooltip{- \frac{1}{2}}{<A3 B1>} \\ \hdashline \tooltip{0}{<B2>} & \tooltip{0}{<A1 B2>} & \tooltip{\frac{1}{2}}{<A2 B2>} & \tooltip{- \frac{1}{2}}{<A3 B2>}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } \frac{1}{2} \text{ } P(11|21) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(21|21) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(11|31) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(21|31) \\ \frac{1}{2} \text{ } P(12|21) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(22|21) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(12|31) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(22|31) \\ \frac{1}{2} \text{ } P(11|22) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(21|22) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(11|32) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(21|32) \\ \text{-} \text{ } \frac{1}{2} \text{ } P(12|22) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(22|22) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(12|32) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(22|32)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } 1 \text{ } P_(|) \text{ } \text{+} \text{ } 2 \text{ } P_A(1|3) \text{ } \text{+} \text{ } 2 \text{ } P_B(1|1) \text{ } \text{-} \text{ } 2 \text{ } P_AB(1,1|2,1) \\ \text{-} \text{ } 2 \text{ } P_AB(1,1|3,1) \text{ } \text{+} \text{ } 2 \text{ } P_AB(1,1|2,2) \text{ } \text{-} \text{ } 2 \text{ } P_AB(1,1|3,2)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\text{-} \text{ } \frac{1}{2} \text{ } <A2 B1> \text{ } \text{-} \text{ } \frac{1}{2} \text{ } <A3 B1> \text{ } \text{+} \text{ } \frac{1}{2} \text{ } <A2 B2> \text{ } \text{-} \text{ } \frac{1}{2} \text{ } <A3 B2>\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$

Symmetry group

Symmetry group of order: 16

Generators:

  • liftings :
    • A1(1,2)
  • outputPerms :
    • A2(1,2) A3(1,2) B1(1,2) B2(1,2)
  • outputInputPerms :
    • A2(1,2) B(1,2)
    • B2(1,2) A(2,3)

Extras