Local models with hidden variables for a K0 system

G. C. Scallera

F. Selleri

1 History of the Einstein-Podolsky-Rosen Paradox.- 2 Are Faster-Than-Light Influences Necessary?.- 3 All the Inequalities of Einstein Locality.- 4 Einstein-Podolsky-Rosen Experiments Using the Decays of ?c or J/? into ??? ? ?-?p?+p?.- Chapter5 Einstein-Podolsky-Rosen Paradox for the K0-K?0 and B0-B?0 Systems.- 6 Even Local Probabilities Lead to the Paradox.- 7 The Experimental Investigation of the Einstein-Podolsky-Rosen Question and Bell's Inequality.- 8 Rapisarda's Experiment: Testing Quantum Mechanics versus Local Hidden-Variable Theories with Dichotomic Analyzers.- 9 Nonlocality and the Einstein-Podolsky-Rosen Experiment as Understood through the Quantum-Potential Approach.- 10 Interpretation of the Einstein-Podolsky-Rosen Effect in Terms of a Generalized Causality.- 11 Quantum Action-at-a-Distance: The Mystery of Einstein-Podolsky-Rosen Correlations.- 12 Particle Trajectories and Quantum Correlations.- 13 Bell's Inequality and the Nonergodic Interpretation of Quantum Mechanics.- 14 An Extended-Probability Response to the Einstein-Podolsky-Rosen Argument.- 15 The Search for Hidden Variables in Quantum Mechanics.- 16 Variable Detection Probability Models for Einstein-Podolsky-Rosen-Type Experiments.- 17 Stochastic Electrodynamics and the Einstein-Podolsky-Rosen Argument.- 18 Explicit Calculations with a Hidden-Variable Spin Model.- 19 Symmetric and Asymmetric Models for Atomic Cascade Experiments.

Peter J. Lewis

Gianni Garbarino

In this talk we discuss the predictions of local realistic theories for the evolution of a K0-K0bar quantum entangled pair created in the decay of the phi-meson. It is shown, in agreement with Bell's theorem, that the most general local hidden-variable model fails in reproducing the whole set of quantum-mechanical observables. We achieve this conclusion by employing two different approaches. In the first approach, the local realistic observables are deduced from the most general premises concerning locality and realism, and Bell-like inequalities are not employed. The other approach makes use of Bell's inequalities. Under particular conditions for the detection times, within the first approach the discrepancy between quantum mechanics and local realism for the asymmetry parameter turns out to be not less than 20%. A similar incompatibility can be made evident by means of a Bell-type test, by employing a Clauser-Horne-Shimony-Holt's inequality written in terms of properly normalized observables. Because of its relatively low experimental accuracy, the data obtained by the CPLEAR collaboration do not yet allow a decisive test of local realism. Such a test, both with and without the use of Bell's inequalities, should be feasible in the future at the Frascati Phi-factory.

K. Fujikawa

It is pointed out that the local hidden-variable model of Bell and Clauser-Horne-Shimony-Holt (CHSH) gives |≪B >| ≤2√2 or |≪B >| ≤2 for the quantum CHSH operator B = a·σ ⊗(b + b′) ·σ + a′ ·σ ⊗ (b - b′) ·σ depending on two different ways of evaluation, when it is applied to a d = 4 system of two spin-1/2 particles. This is due to the failure of linearity, and it shows that the conventional CHSH inequality |≪B >| ≤2 does not provide a reliable test of the d = 4 local non-contextual hidden-variable model. To achieve |≪B >| ≤2 uniquely, one needs to impose a linearity requirement on the hidden-variable model, which in turn adds a von Neumann-type stricture. It is then shown that the local model is converted to a factored product of two non-contextual d = 2 hidden-variable models. This factored product implies pure separable quantum states and satisfies |≪B >| ≤2, but no more a proper hidden-variable model in d = 4. The conventional CHSH inequality |≪B >| ≤2 thus characterizes the pure separable quantum mechanical states but does not test the model of local hidden variables in d = 4, to be consistent with Gleason's theorem which excludes non-contextual models in d = 4. This observation is also consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to hidden variables.