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A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed rather than restricting the possible measurements to projective ones.
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According to the definition introduced in Ref. [ 11 ] , a two-dimensional witness is a vector w → \vec{w} of real coefficients, such that w → ⋅ p → = ∑ a , b , x , y w a b x y p ( a b | x y ) ≤ w 2 \vec{w}\cdot\vec{p}=\sum_{a,b,x,y}w_{abxy}p(ab|xy)\leq w_{2} for all probabilities p ( a b | x y ) p(ab|xy) expressed by formula ( 1
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J. Sturm, SeDuMi, a MATLAB toolbox for optimization over symmetric cones, URL http://sedumi.mcmaster.ca
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