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arXiv:hep-ph/0609251 · Frascati Phys.Ser.

Strangeness measurements of kaon pairs, CP violation and Bell inequalities

Reinhold A. Bertlmann, Beatrix C. Hiesmayr

Published Sep 25, 2006• 34 citations
arXivHTMLPDF

Abstract

The nonlocal property of quantum mechanics can be nicely tested in high energy physics; in particular, the neutral kaon pairs as produced at DA$Φ$NE, Frascati, are very well suited. The analogies of kaons as compared to polarized photons or spin--1/2 particles --the kaonic qubit feature-- are reviewed. However, there are also fundamental differences which occur due to the kaon time evolution and due to internal symmetries; in particular, the violation of CP symmetry is related to the violation of Bell inequalities. Two type of Bell inequalities for kaons are presented, one for the variation of the ``quasi--spin'' and the other for different detection times of the kaon.

DOI
10.48550/arxiv.hep-ph/0609251

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The nonlocal property of quantum mechanics can be nicely tested in high energy physics; in particular, the neutral kaon pairs as produced at DAΦΦΦNE, Frascati, are very well suited. The analogies of kaons as compared to polarized photons or spin--1/2 particles --the kaonic qubit feature-- are reviewed. However, there are also fundamental differences which occur due to the kaon time evolution and due to internal symmetries; in particular, the violation of CP symmetry is related to the violation of Bell inequalities. Two type of Bell inequalities for kaons are presented, one for the variation of the ``quasi--spin'' and the other for different detection times of the kaon.
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Testing quantum foundations for systems in high energy physics gets currently more and more attention e.g. witnessed for entangled neutral K‐mesons by the approved programme of the KLOE collaboration at the accelerator facility DAPHNE (Frascati, Italy). We focus on this quantum system in high energy physics and discuss two topics, Bell inequalities and the kaonic quantum eraser, and show how the neutral kaon system differs from systems of ordinary matter and light. In detail, we show a relation of the imbalance of matter and antimatter to the violation of a Bell inequality and discuss another Bell inequality which is maximally violated for a non‐maximally entangled state though neutral kaons can be considered as two state systems. We compare in general this system in high energy physics with bipartite qudits. Last but not least we review the quantum marking and eraser procedure and explain why neutral kaons offer more eraser possibilities than usual quantum systems.
Testing quantum foundations for systems in high energy physics gets currently more and more attention e.g. witnessed for entangled neutral K‐mesons by the approved programme of the KLOE collaboration at the accelerator facility DAPHNE (Frascati, Italy). We focus on this quantum system in high energy physics and discuss two topics, Bell inequalities and the kaonic quantum eraser, and show how the neutral kaon system differs from systems of ordinary matter and light. In detail, we show a relation of the imbalance of matter and antimatter to the violation of a Bell inequality and discuss another Bell inequality which is maximally violated for a non‐maximally entangled state though neutral kaons can be considered as two state systems. We compare in general this system in high energy physics with bipartite qudits. Last but not least we review the quantum marking and eraser procedure and explain why neutral kaons offer more eraser possibilities than usual quantum systems.
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We investigate Bell inequalities for neutral kaon systems from $\ensuremath{\Phi}$ resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, which means we also include all decay product states, in contrast to other authors. Only this guarantees the use of the complete Hilbert space. We develop a general formalism for Bell inequalities including both arbitrary ``quasispin'' states and different times; finally, we analyze Wigner-type inequalities. They contain an additional term, a correction function h, as compared to the spin 1/21/21/2 or photon case, which changes considerably the possibility of quantum mechanics to violate the Bell inequality. Examples for special ``quasispin'' states are given, especially those that are sensitive to the CP\mathrm{CP}CP parameters $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}^{\ensuremath{'}}.$