Scenario

[(2 2 2) (2 2 2)]

Description

I3322/I3322, defined in Collins, Gisin 2004.

Cross references

#4

Bell expression and bounds

$$ \left (\begin{array}{rr:rr:rr} \tooltip{\frac{5}{36}}{P(11|11)} & \tooltip{- \frac{19}{36}}{P(21|11)} & \tooltip{\frac{5}{36}}{P(11|21)} & \tooltip{- \frac{19}{36}}{P(21|21)} & \tooltip{\frac{1}{18}}{P(11|31)} & \tooltip{- \frac{4}{9}}{P(21|31)} \\ \tooltip{- \frac{7}{36}}{P(12|11)} & \tooltip{\frac{5}{36}}{P(22|11)} & \tooltip{- \frac{7}{36}}{P(12|21)} & \tooltip{\frac{5}{36}}{P(22|21)} & \tooltip{- \frac{5}{18}}{P(12|31)} & \tooltip{\frac{2}{9}}{P(22|31)} \\ \hdashline \tooltip{\frac{5}{36}}{P(11|12)} & \tooltip{- \frac{19}{36}}{P(21|12)} & \tooltip{\frac{5}{36}}{P(11|22)} & \tooltip{- \frac{19}{36}}{P(21|22)} & \tooltip{- \frac{4}{9}}{P(11|32)} & \tooltip{\frac{1}{18}}{P(21|32)} \\ \tooltip{- \frac{7}{36}}{P(12|12)} & \tooltip{\frac{5}{36}}{P(22|12)} & \tooltip{- \frac{7}{36}}{P(12|22)} & \tooltip{\frac{5}{36}}{P(22|22)} & \tooltip{\frac{2}{9}}{P(12|32)} & \tooltip{- \frac{5}{18}}{P(22|32)} \\ \hdashline \tooltip{\frac{2}{9}}{P(11|13)} & \tooltip{- \frac{4}{9}}{P(21|13)} & \tooltip{- \frac{5}{18}}{P(11|23)} & \tooltip{\frac{1}{18}}{P(21|23)} & \tooltip{- \frac{1}{9}}{P(11|33)} & \tooltip{- \frac{1}{9}}{P(21|33)} \\ \tooltip{- \frac{5}{18}}{P(12|13)} & \tooltip{\frac{1}{18}}{P(22|13)} & \tooltip{\frac{2}{9}}{P(12|23)} & \tooltip{- \frac{4}{9}}{P(22|23)} & \tooltip{- \frac{1}{9}}{P(12|33)} & \tooltip{- \frac{1}{9}}{P(22|33)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 0\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|r:r:r} & \tooltip{-1}{P_A(1|1)} & \tooltip{0}{P_A(1|2)} & \tooltip{0}{P_A(1|3)} \\ \hline \tooltip{-2}{P_B(1|1)} & \tooltip{1}{P_AB(1,1|1,1)} & \tooltip{1}{P_AB(1,1|2,1)} & \tooltip{1}{P_AB(1,1|3,1)} \\ \hdashline \tooltip{-1}{P_B(1|2)} & \tooltip{1}{P_AB(1,1|1,2)} & \tooltip{1}{P_AB(1,1|2,2)} & \tooltip{-1}{P_AB(1,1|3,2)} \\ \hdashline \tooltip{0}{P_B(1|3)} & \tooltip{1}{P_AB(1,1|1,3)} & \tooltip{-1}{P_AB(1,1|2,3)} & \tooltip{0}{P_AB(1,1|3,3)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 0\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|r:r:r} \tooltip{-1}{<>} & \tooltip{\frac{1}{4}}{<A1>} & \tooltip{\frac{1}{4}}{<A2>} & \tooltip{0}{<A3>} \\ \hline \tooltip{- \frac{1}{4}}{<B1>} & \tooltip{\frac{1}{4}}{<A1 B1>} & \tooltip{\frac{1}{4}}{<A2 B1>} & \tooltip{\frac{1}{4}}{<A3 B1>} \\ \hdashline \tooltip{- \frac{1}{4}}{<B2>} & \tooltip{\frac{1}{4}}{<A1 B2>} & \tooltip{\frac{1}{4}}{<A2 B2>} & \tooltip{- \frac{1}{4}}{<A3 B2>} \\ \hdashline \tooltip{0}{<B3>} & \tooltip{\frac{1}{4}}{<A1 B3>} & \tooltip{- \frac{1}{4}}{<A2 B3>} & \tooltip{0}{<A3 B3>}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 0\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \frac{5}{36} \text{ } P(11|11) \text{ } \text{-} \text{ } \frac{19}{36} \text{ } P(21|11) \text{ } \text{+} \text{ } \frac{5}{36} \text{ } P(11|21) \text{ } \text{-} \text{ } \frac{19}{36} \text{ } P(21|21) \\ \frac{1}{18} \text{ } P(11|31) \text{ } \text{-} \text{ } \frac{4}{9} \text{ } P(21|31) \text{ } \text{-} \text{ } \frac{7}{36} \text{ } P(12|11) \text{ } \text{+} \text{ } \frac{5}{36} \text{ } P(22|11) \\ \text{-} \text{ } \frac{7}{36} \text{ } P(12|21) \text{ } \text{+} \text{ } \frac{5}{36} \text{ } P(22|21) \text{ } \text{-} \text{ } \frac{5}{18} \text{ } P(12|31) \text{ } \text{+} \text{ } \frac{2}{9} \text{ } P(22|31) \\ \frac{5}{36} \text{ } P(11|12) \text{ } \text{-} \text{ } \frac{19}{36} \text{ } P(21|12) \text{ } \text{+} \text{ } \frac{5}{36} \text{ } P(11|22) \text{ } \text{-} \text{ } \frac{19}{36} \text{ } P(21|22) \\ \text{-} \text{ } \frac{4}{9} \text{ } P(11|32) \text{ } \text{+} \text{ } \frac{1}{18} \text{ } P(21|32) \text{ } \text{-} \text{ } \frac{7}{36} \text{ } P(12|12) \text{ } \text{+} \text{ } \frac{5}{36} \text{ } P(22|12) \\ \text{-} \text{ } \frac{7}{36} \text{ } P(12|22) \text{ } \text{+} \text{ } \frac{5}{36} \text{ } P(22|22) \text{ } \text{+} \text{ } \frac{2}{9} \text{ } P(12|32) \text{ } \text{-} \text{ } \frac{5}{18} \text{ } P(22|32) \\ \frac{2}{9} \text{ } P(11|13) \text{ } \text{-} \text{ } \frac{4}{9} \text{ } P(21|13) \text{ } \text{-} \text{ } \frac{5}{18} \text{ } P(11|23) \text{ } \text{+} \text{ } \frac{1}{18} \text{ } P(21|23) \\ \text{-} \text{ } \frac{1}{9} \text{ } P(11|33) \text{ } \text{-} \text{ } \frac{1}{9} \text{ } P(21|33) \text{ } \text{-} \text{ } \frac{5}{18} \text{ } P(12|13) \text{ } \text{+} \text{ } \frac{1}{18} \text{ } P(22|13) \\ \frac{2}{9} \text{ } P(12|23) \text{ } \text{-} \text{ } \frac{4}{9} \text{ } P(22|23) \text{ } \text{-} \text{ } \frac{1}{9} \text{ } P(12|33) \text{ } \text{-} \text{ } \frac{1}{9} \text{ } P(22|33)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 0\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } 1 \text{ } P_A(1|1) \text{ } \text{-} \text{ } 2 \text{ } P_B(1|1) \text{ } \text{+} \text{ } 1 \text{ } P_AB(1,1|1,1) \text{ } \text{+} \text{ } 1 \text{ } P_AB(1,1|2,1) \\ 1 \text{ } P_AB(1,1|3,1) \text{ } \text{-} \text{ } 1 \text{ } P_B(1|2) \text{ } \text{+} \text{ } 1 \text{ } P_AB(1,1|1,2) \text{ } \text{+} \text{ } 1 \text{ } P_AB(1,1|2,2) \\ \text{-} \text{ } 1 \text{ } P_AB(1,1|3,2) \text{ } \text{+} \text{ } 1 \text{ } P_AB(1,1|1,3) \text{ } \text{-} \text{ } 1 \text{ } P_AB(1,1|2,3)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 0\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } 1 \text{ } <> \text{ } \text{+} \text{ } \frac{1}{4} \text{ } <A1> \text{ } \text{+} \text{ } \frac{1}{4} \text{ } <A2> \text{ } \text{-} \text{ } \frac{1}{4} \text{ } <B1> \\ \frac{1}{4} \text{ } <A1 B1> \text{ } \text{+} \text{ } \frac{1}{4} \text{ } <A2 B1> \text{ } \text{+} \text{ } \frac{1}{4} \text{ } <A3 B1> \text{ } \text{-} \text{ } \frac{1}{4} \text{ } <B2> \\ \frac{1}{4} \text{ } <A1 B2> \text{ } \text{+} \text{ } \frac{1}{4} \text{ } <A2 B2> \text{ } \text{-} \text{ } \frac{1}{4} \text{ } <A3 B2> \text{ } \text{+} \text{ } \frac{1}{4} \text{ } <A1 B3> \\ \text{-} \text{ } \frac{1}{4} \text{ } <A2 B3>\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 0\text{ (facet)}\end{array} \right. $$

Symmetry group

Symmetry group of order: 8

Generators:

  • outputInputPerms :
    • A3(1,2) B(1,2)
    • B3(1,2) A(1,2)
  • rest :
    • A1(1,2) A2(1,2) B1(1,2) B2(1,2) A(1,2) B(1,2) (A,B)

Extras

Sources