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arXiv:quant-ph/0205112 · Physical Review Letters

Test of Local Realism with Entangled Kaon Pairs and without Inequalities

A. Bramòn, Gianni Garbarino

Published Sep 30, 2002• 71 citations
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Abstract

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.

DOI
10.1103/physrevlett.89.160401

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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.
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 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 discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic nonmaximally entangled two-qubit state and two incompatible bases to be adopted for alternative measurements of two observables $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$ and $\mathrm{b\ifmmode \hat{}\else \^{}\fi{}}$ on each party, we apply Hardy's proof of nonlocality without inequality and derive an Eberhard-like inequality. For an infinity of nonmaximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two observables, say $\mathrm{b\ifmmode \hat{}\else \^{}\fi{}}$, to be measured on each party: The test is free from the detection loophole for any value of the detection efficiency corresponding to the other observable $\mathrm{a\ifmmode \hat{}\else \^{}\fi{}}$. The maximum tolerable noise in such a loophole-free observable-asymmetric test is also evaluated.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
Bell's theorem states that the quantum mechanical description of physical quantities cannot be fully explained by local realistic theories, laying a solid basis for various quantum information applications. Hardy's paradox is celebrated as the simplest form of Bell's theorem concerning its "All versus Nothing" approach to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of the experimental systems, and these assumptions constitute potential loopholes for faithfully testing local realistic theories. Here, we experimentally demonstrate Hardy's nonlocality through a photonic entanglement source. By achieving a detection efficiency of 82.2%, a quantum state fidelity of 99.10%, and applying high-speed quantum random number generators for the measurement setting switching, the experiment is implemented in a loophole-free manner. During 6 h of running, a strong violation of P_{Hardy}=4.646×10^{-4} up to 5 standard deviations is observed with 4.32×10^{9} trials. A null hypothesis test shows that the results can be explained by local realistic theories with an upper bound probability of 10^{-16348}. These testing results provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.