Entanglement in single-neutron system

Non-local correlations between subsystems sufficiently separated in space-time have been extensively discussed in the light of the Einstein, Podolsky, and Rosen (EPR) paradox, together with the Bell's inequality. Within quantum terminology, such a non- locality can be interpreted as a consequence of the entanglement of subsystems as well as commuting observables due to the different position. Thus, a more general concept, i.e., contextuality, compared to non-locality can be introduced to describe other striking phenomena predicted by quantum theory. As an example of quantum contextuality, we report a neutron interferometer experiment which clearly demonstrates the violation of a Bell-like inequality. Entanglement is achieved not between particles, but between the degrees of freedom i.e., spin and path, in this case, for a single-particle. Appropriate combinations of the direction of spin analysis and the position of the phase shifter allow an experimental verification of the violation of a Bell-like inequality. In addition, experimental results of so-called state tomography, tomographic analysis of the density matrix of a quantum system, are presented to characterize neutrons¡Ç entangled states. These experiments manifest high fidelities, up to 91%, of the entangled neutrons¡Ç states. Finally, we are going to describe new possibilities to implement a multi- entanglement in single-neutrons.
Y. Hasegawa et al., Nature 425 (2003) 45-48.
Y. Hasegawa et al., Phys. Rev. Lett. 97 (2006) 230401.