Knowledge excess duality and violation of Bell inequalities: Theory and experiment

摘要

We analyze correlations between two parties sharing a general mixed two-qubit state rho(SM) 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 excesses Delta K(Pi(M) -> Pi(S)) and Delta K(Pi'(M) -> Pi'(S)) are used, where Pi(S), Pi'(S) resp. Pi(M), Pi'(M) represent projective measurements on the qubit S resp. M. We derive an inequality Delta K-2(Pi(M) -> Pi(S)) + Delta K-2(Pi'(M), Pi'(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 rho(SM) and for arbitrary Pi(S), Pi'(S) and Pi'(M), Pi'(M). This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.