We analyze correlations between two parties sharing a general mixed two-qubit state ρSM in order to predict measurement outcomes. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on one qubit from the measurement results on the other qubit. To quantify these predictions the complementary knowledge excessesΔK(ΠM→ΠS) and ΔK(Π′M→Π′S) are used, where ΠS, Π′S resp. ΠM, Π′M represent projective measurements on the qubit S resp. M. We derive an inequality ΔK2(ΠM→ΠS) + ΔK2(Π′M→Π′S)≤(B max /2)2, where B max is the maximum violation of Bell inequalities. This inequality restricts our capability to enhance the complementary predictions for any state ρSM and for arbitrary ΠS, Π′S and ΠM, Π′M. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.
Partial Bell-State Analysis with Parametric down Conversion in the Wigner Function Formalism