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Physical Review A

Quantum mechanics versus local realism for neutral kaon pairs

Roshan Foadi, F. Selleri

Published Dec 13, 1999• 51 citations
Publisher

Abstract

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 $\mathrm{CP}$ 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 ${K}^{0}{K}^{0}$ pairs at certain different proper times turns out to differ considerably from the quantum-mechanical predictions.

DOI
10.1103/physreva.61.012106

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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 \ensuremathφ\ensuremath{\varphi}\ensuremathφ 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 realistic theory of single neutral kaons and of correlated neutral kaon pairs is formulated by deducing the most general consequences of three assumptions: (i) the Einstein-Podolsky-Rosen (EPR) reality criterion, (ii) locality, and (iii) no retroactive causality. Variables must be introduced for every kaon determining the stable CP\mathrm{CP}CP value and the variable value of strangeness S.S.S. Instantaneous SSS jumps are shown to take place. If kaon pairs are produced in \ensuremath{\Phi} meson decays, the local realistic probability of observing K‾0K‾0{\overline{K}}^{0}{\overline{K}}^{0}K0K0 pairs at certain different proper times necessarily differs by 30% from the quantum-mechanical predictions. The size of this difference justifies our systematic neglect of CP\mathrm{CP}CP violation. A \ensuremath{\Phi} factory is thus shown to provide a unique tool for the study of the EPR problem
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.
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.
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.
The quantum interference between the decays of entangled neutral kaons is a very powerful tool for testing the quantum coherence of the entangled kaon pair state. The studied process ϕ→KSKL→π+π−π+π−\phi\rightarrow K_SK_L\rightarrow\pi^+\pi^-\pi^+\pi^-ϕ→KS​KL​→π+π−π+π− exhibits the characteristic Einstein-Podolsky-Rosen correlations that prevent both kaons to decay into π+π−\pi^+\pi^-π+π− at the same time. The newly published result is based on data sample collected with the KLOE detector at DAΦ\PhiΦNE and corresponds to an integrated luminosity of about 1.7 fb−1^{-1}−1 , i.e. to ∼\sim∼ 1.7 ×\times× 109^99 ϕ→KSKL\phi\rightarrow K_SK_Lϕ→KS​KL​ decays. From the fit to the observed time difference distribution of the two kaon decays, the decoherence and CPT violation parameters of various phenomenological models are measured. A stringent upper limit on the branching ratio of the ϕ→KSKS,KLKL\phi \rightarrow K_S K_S , K_L K_Lϕ→KS​KS​,KL​KL​ decay is also derived. Independently, the comparison of neutral meson transition rates between flavour and CP eigenstates allows direct and model independent tests of time-reversal T and CPT symmetries to be conducted, through ratios of rates of two classes of processes: KSKL→(π±e∓ν)(3π0)K_S K_L \to (\pi^{\pm}e^{\mp}\nu)(3\pi^0)KS​KL​→(π±e∓ν)(3π0) and KSKL→(π+π−)(π±e∓ν)K_S K_L \to (\pi^{+}\pi^{-})(\pi^{\pm}e^{\mp}\nu)KS​KL​→(π+π−)(π±e∓ν). In addition to this a straightforward extension to the case of CPT symmetry is performed providing the first model independent test of CPT symmetry violation in transitions of neutral kaons.