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arXiv:quant-ph/0305087 · Physical Review A

Entanglement properties of kaons and tests of hidden-variable models

Marco Genovese

Published Feb 11, 2004• 19 citations
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Abstract

In this paper we discuss entanglement properties of neutral kaons systems and their use for testing local realism. In particular, we analyze a Hardy-type scheme [A. Bramon and G. Garbarino, Phys. Rev. Lett. 89, 160401 (2002)] recently suggested for performing a test of hidden-variable theories against standard quantum mechanics. Our result is that this scheme could, in principle, lead to a conclusive test of local realism, but only if higher identification efficiencies than in today's experiments will be reached.

DOI
10.1103/physreva.69.022103

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In this paper we discuss entanglement properties of neutral kaons systems and their use for testing local realism. In particular, we analyze a Hardy-type scheme [A. Bramon and G. Garbarino, Phys. Rev. Lett. 89, 160401 (2002)] recently suggested for performing a test of hidden-variable theories against standard quantum mechanics. Our result is that this scheme could, in principle, lead to a conclusive test of local realism, but only if higher identification efficiencies than in today's experiments will be reached.
We shortly review a couple of proposals of Bell inequality tests with entangled pairs of neutral kaons from φ resonance decays.The suggested experiments are discussed in the light of the essential requirements for a genuine discrimination between local hidden-variable theories (i.e., local realism) and quantum mechanics.We clarify the logical limitations of these tests in refuting the whole class of local realistic models.Detailed analyses imply that a Bell-type test with neutral kaons free from the detection loophole requires a few % strangeness detection efficiencies and very high efficiencies for the detection of the kaon decay products.
We propose the use of entangled pairs of neutral kaons, considered as a promising tool to close the well known loopholes affecting generic Bell's inequality tests, in a specific Hardy-type experiment. Hardy's contradiction without inequalities between local realism and quantum mechanics can be translated into a feasible experiment by requiring ideal detection efficiencies for only one of the observables to be alternatively measured. Neutral kaons are near to fulfill this requirement and therefore to close the efficiency loophole.
A local realistic theory of single neutral kaons and of correlated neutral kaon pairs was formulated [F. Selleri, Phys. Rev. A 56, 3493 (1997)] by deducing the consequences of three assumptions: (i) Einstein-Podolsky-Rosen reality criterion; (ii) locality; (iii) lack of retroactive causality. Variables were introduced for every kaon determining the stable CP\mathrm{CP}CP value and the changing value of strangeness S. That theory is here generalized by taking into full account the history-dependent nature of kaons. If kaon pairs are produced in $\ensuremath{\varphi}$ meson decays, the local realistic probability of observing K0K0{K}^{0}{K}^{0}K0K0 pairs at certain different proper times turns out to differ considerably from the quantum-mechanical predictions.
A local hidden-variable model is exhibited for the experiments by Aspect, Grangier, and Roger [Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982)] and Aspect, Dalibard, and Roger [Phys. Rev. Lett. 49, 1804 (1982)] measuring polarization correlation of optical-photon pairs. The model agrees with quantum-mechanical predictions for all measurable quantities even with ideal polarizers and detectors, and emphasizes the need of a high degree of directional correlation, besides the correlation of spin (or polarization or other quantities), in any test of locality. It is proved that homogeneous inequalities, involving only coincidence detection rates, cannot discriminate between quantum mechanics and local theories, which invalidates all previously used empirical tests. The role of supplementary assumptions, like the so-called no enhancement, for the derivation of Bell's inequalities is discussed. Finally it is conjectured that quantum mechanics might be compatible with local realism, if we assume that not all self-adjoint operators represent observables and not all density operators represent states.