Scenario

[(3 3 2) (3 2)]

Description

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

Cross references

#3

Bell expression and bounds

$$ \left (\begin{array}{rrr:rr} \tooltip{- \frac{25}{51}}{P(11|11)} & \tooltip{- \frac{25}{51}}{P(21|11)} & \tooltip{\frac{38}{51}}{P(31|11)} & \tooltip{- \frac{4}{51}}{P(11|21)} & \tooltip{- \frac{4}{51}}{P(21|21)} & \tooltip{- \frac{4}{51}}{P(31|21)} & \tooltip{- \frac{71}{102}}{P(11|31)} & \tooltip{\frac{55}{102}}{P(21|31)} \\ \tooltip{\frac{1}{3}}{P(12|11)} & \tooltip{\frac{1}{3}}{P(22|11)} & \tooltip{- \frac{28}{51}}{P(32|11)} & \tooltip{\frac{2}{51}}{P(12|21)} & \tooltip{\frac{2}{51}}{P(22|21)} & \tooltip{\frac{2}{51}}{P(32|21)} & \tooltip{\frac{49}{102}}{P(12|31)} & \tooltip{- \frac{41}{102}}{P(22|31)} \\ \tooltip{\frac{1}{3}}{P(13|11)} & \tooltip{\frac{1}{3}}{P(23|11)} & \tooltip{- \frac{28}{51}}{P(33|11)} & \tooltip{\frac{2}{51}}{P(13|21)} & \tooltip{\frac{2}{51}}{P(23|21)} & \tooltip{\frac{2}{51}}{P(33|21)} & \tooltip{\frac{49}{102}}{P(13|31)} & \tooltip{- \frac{41}{102}}{P(23|31)} \\ \hdashline \tooltip{\frac{8}{17}}{P(11|12)} & \tooltip{\frac{8}{17}}{P(21|12)} & \tooltip{- \frac{13}{17}}{P(31|12)} & \tooltip{\frac{1}{17}}{P(11|22)} & \tooltip{\frac{1}{17}}{P(21|22)} & \tooltip{\frac{1}{17}}{P(31|22)} & \tooltip{- \frac{13}{34}}{P(11|32)} & \tooltip{\frac{1}{2}}{P(21|32)} \\ \tooltip{- \frac{6}{17}}{P(12|12)} & \tooltip{- \frac{6}{17}}{P(22|12)} & \tooltip{\frac{9}{17}}{P(32|12)} & \tooltip{- \frac{1}{17}}{P(12|22)} & \tooltip{- \frac{1}{17}}{P(22|22)} & \tooltip{- \frac{1}{17}}{P(32|22)} & \tooltip{\frac{19}{34}}{P(12|32)} & \tooltip{- \frac{23}{34}}{P(22|32)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|rr:r} \tooltip{- \frac{19}{17}}{P_(|)} & \tooltip{0}{P_A(1|1)} & \tooltip{0}{P_A(2|1)} & \tooltip{0}{P_A(1|2)} & \tooltip{0}{P_A(2|2)} & \tooltip{\frac{36}{17}}{P_A(1|3)} \\ \hline \tooltip{\frac{36}{17}}{P_B(1|1)} & \tooltip{- \frac{36}{17}}{P_AB(1,1|1,1)} & \tooltip{- \frac{36}{17}}{P_AB(2,1|1,1)} & \tooltip{0}{P_AB(1,1|2,1)} & \tooltip{0}{P_AB(2,1|2,1)} & \tooltip{- \frac{36}{17}}{P_AB(1,1|3,1)} \\ \tooltip{0}{P_B(2|1)} & \tooltip{0}{P_AB(1,2|1,1)} & \tooltip{0}{P_AB(2,2|1,1)} & \tooltip{0}{P_AB(1,2|2,1)} & \tooltip{0}{P_AB(2,2|2,1)} & \tooltip{0}{P_AB(1,2|3,1)} \\ \hdashline \tooltip{0}{P_B(1|2)} & \tooltip{\frac{36}{17}}{P_AB(1,1|1,2)} & \tooltip{\frac{36}{17}}{P_AB(2,1|1,2)} & \tooltip{0}{P_AB(1,1|2,2)} & \tooltip{0}{P_AB(2,1|2,2)} & \tooltip{- \frac{36}{17}}{P_AB(1,1|3,2)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } \frac{25}{51} \text{ } P(11|11) \text{ } \text{-} \text{ } \frac{25}{51} \text{ } P(21|11) \text{ } \text{+} \text{ } \frac{38}{51} \text{ } P(31|11) \text{ } \text{-} \text{ } \frac{4}{51} \text{ } P(11|21) \\ \text{-} \text{ } \frac{4}{51} \text{ } P(21|21) \text{ } \text{-} \text{ } \frac{4}{51} \text{ } P(31|21) \text{ } \text{-} \text{ } \frac{71}{102} \text{ } P(11|31) \text{ } \text{+} \text{ } \frac{55}{102} \text{ } P(21|31) \\ \frac{1}{3} \text{ } P(12|11) \text{ } \text{+} \text{ } \frac{1}{3} \text{ } P(22|11) \text{ } \text{-} \text{ } \frac{28}{51} \text{ } P(32|11) \text{ } \text{+} \text{ } \frac{2}{51} \text{ } P(12|21) \\ \frac{2}{51} \text{ } P(22|21) \text{ } \text{+} \text{ } \frac{2}{51} \text{ } P(32|21) \text{ } \text{+} \text{ } \frac{49}{102} \text{ } P(12|31) \text{ } \text{-} \text{ } \frac{41}{102} \text{ } P(22|31) \\ \frac{1}{3} \text{ } P(13|11) \text{ } \text{+} \text{ } \frac{1}{3} \text{ } P(23|11) \text{ } \text{-} \text{ } \frac{28}{51} \text{ } P(33|11) \text{ } \text{+} \text{ } \frac{2}{51} \text{ } P(13|21) \\ \frac{2}{51} \text{ } P(23|21) \text{ } \text{+} \text{ } \frac{2}{51} \text{ } P(33|21) \text{ } \text{+} \text{ } \frac{49}{102} \text{ } P(13|31) \text{ } \text{-} \text{ } \frac{41}{102} \text{ } P(23|31) \\ \frac{8}{17} \text{ } P(11|12) \text{ } \text{+} \text{ } \frac{8}{17} \text{ } P(21|12) \text{ } \text{-} \text{ } \frac{13}{17} \text{ } P(31|12) \text{ } \text{+} \text{ } \frac{1}{17} \text{ } P(11|22) \\ \frac{1}{17} \text{ } P(21|22) \text{ } \text{+} \text{ } \frac{1}{17} \text{ } P(31|22) \text{ } \text{-} \text{ } \frac{13}{34} \text{ } P(11|32) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(21|32) \\ \text{-} \text{ } \frac{6}{17} \text{ } P(12|12) \text{ } \text{-} \text{ } \frac{6}{17} \text{ } P(22|12) \text{ } \text{+} \text{ } \frac{9}{17} \text{ } P(32|12) \text{ } \text{-} \text{ } \frac{1}{17} \text{ } P(12|22) \\ \text{-} \text{ } \frac{1}{17} \text{ } P(22|22) \text{ } \text{-} \text{ } \frac{1}{17} \text{ } P(32|22) \text{ } \text{+} \text{ } \frac{19}{34} \text{ } P(12|32) \text{ } \text{-} \text{ } \frac{23}{34} \text{ } P(22|32)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } \frac{19}{17} \text{ } P_(|) \text{ } \text{+} \text{ } \frac{36}{17} \text{ } P_A(1|3) \text{ } \text{+} \text{ } \frac{36}{17} \text{ } P_B(1|1) \text{ } \text{-} \text{ } \frac{36}{17} \text{ } P_AB(1,1|1,1) \\ \text{-} \text{ } \frac{36}{17} \text{ } P_AB(2,1|1,1) \text{ } \text{-} \text{ } \frac{36}{17} \text{ } P_AB(1,1|3,1) \text{ } \text{+} \text{ } \frac{36}{17} \text{ } P_AB(1,1|1,2) \text{ } \text{+} \text{ } \frac{36}{17} \text{ } P_AB(2,1|1,2) \\ \text{-} \text{ } \frac{36}{17} \text{ } P_AB(1,1|3,2)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$

Symmetry group

Symmetry group of order: 24

Generators:

  • liftings :
    • B1(2,3)
    • A2(1,2)
    • A2(2,3)
    • A1(1,2)

Extras