Local realistic theories and quantum mechanics for the two-neutral-kaon system

The predictions of local realistic theories for the observables concerning the evolution of a K-0(K) over bar (0) quantum entangled pair (created in t he decay of the (P-meson) are discussed. It is shown, in agreement with Bel l's theorem, that the most general local hidden-variable model fails in rep roducing the whole set of quantum-mechanical joint probabilities. We achiev e these conclusion by employing two different approaches. In the first appr oach, the local realistic observables are deduced from the most general pre mises concerning locality and realism, and Bell-like inequalities are not e mployed. The other approach makes use of Bell's inequalities. In the first approach, under particular conditions for the detection times, the discrepa ncy between quantum mechanics and local realism for the time-dependent asym metry turns out to be not less than 20%. A similar incompatibility can be m ade evident by means of a Bell-type test by employing both Wigner's and (on ce properly normalized probabilities are used) Clauser-Horne-Shimony-Holt's inequalities. Because of its relatively low experimental accuracy, the dat a obtained by the CPLEAR collaboration for the asymmetry parameter do not y et allow a decisive test of local realism. Such a test, both with and witho ut the use of Bell's inequalities, should be feasible in the future at the Frascati Phi -factory. (C) 2001 Elsevier Science B.V. All rights reserved.