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EPR Test with Photons and Kaons: Analogies

Nicolas Gisin

Published Jan 1, 2008• 57 citations
OpenAlex

Abstract

We present a unified formalism describing EPR test using spin 1/2 particles, photons and kaons. This facilitates the comparison between existing experiments using photons and kaons. It underlines the similarities between birefringence and polarization dependent losses that affects experiments using optical fibers and mixing and decay that are intrinsic to the kaons. We also discuss the limitation these two characteristics impose on the testing of Bell’s inequality. 1

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We present a unified formalism describing EPR test using spin 1/2 particles, photons and kaons. This facilitates the comparison between existing experiments using photons and kaons. It underlines the similarities between birefringence and polarization dependent losses that affects experiments using optical fibers and mixing and decay that are intrinsic to the kaons. We also discuss the limitation these two characteristics impose on the testing of Bell’s inequality. 1
In the early 1950’s, Bohm simplified the 1935 EPR state from continuous coordinate-momentum space to discrete spin space by introducing a singlet state of two spin 1/2 particles. A more practical example of the EPR-Bohm state concerns the polarization states of photon pairs, such as the spin-zero state of a high energy photon pair disintegrated from the annihilation of positronium. Is it possible to have a realistic theory which provides correct predictions of the behavior of a particle similar to quantum theory and, at the same time, respects the description of physical reality by EPR as “complete”? Bohm and his followers have attempted a “hidden variable theory” to formulate the physical reality into the wavefunction of a particle or a pair of particles. The experimental testing of Bell’s inequality started from the early 1970’s. Most of the historical experiments concluded the violation of the Bell’s inequalities and thus disproved the local hidden variable theory.
We extend the use of Bell inequalities to $\ensuremath{\Phi}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}$ decays by exploiting analogies and differences to the well-known and experimentally verified singlet-spin case. Contrasting with other analyses, our Bell inequalities are violated by quantum mechanics and can strictly be derived from local realistic theories. In principle, quantum mechanics could then be tested using unstable, oscillating states governed by a $\mathrm{CP}\ensuremath{-}\mathrm{violating}$ Hamiltonian.
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.