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Physical Review A

Evidence for entanglement and full tomographic analysis of Bell states in a single-neutron system

Yuji Hasegawa, Rudolf Loidl, G. Badurek, Stefan Filipp, Jürgen Klepp, Helmut Rauch

Published Nov 15, 2007• 27 citations
Publisher

Abstract

Tomographic measurements of Bell states of a single-neutron system in an interferometer were carried out. The spin-path joint measurements exhibit clear evidence of entanglement. Reconstructions of the density matrices of, practically complete, Bell states were accomplished. The fidelities as well as the concurrences of the generated states are determined by 0.79 and 0.75 as well as 0.59 and 0.52, respectively, which are again clear evidence of the spin-path entanglement in a single-neutron system.

DOI
10.1103/physreva.76.052108

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Tomographic measurements of Bell states of a single-neutron system in an interferometer were carried out. The spin-path joint measurements exhibit clear evidence of entanglement. Reconstructions of the density matrices of, practically complete, Bell states were accomplished. The fidelities as well as the concurrences of the generated states are determined by 0.79 and 0.75 as well as 0.59 and 0.52, respectively, which are again clear evidence of the spin-path entanglement in a single-neutron system.
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We present experimental evidence of the generation of distinct types of genuine multipartite entanglement between three degrees of freedom (spin, energy and path) within single-neutron quantum systems. This is achieved via the development of new spin manipulation apparatuses for neutron interferometry and the entanglement is detected via appropriately designed and optimized nonlinear witnesses. Via the applied criteria we reveal even finer properties of the type of the genuine multipartite entanglement that is produced in the experiment. In a subsequent analysis we show the extraordinarily high fidelity of the generated entangled states, proving the outstanding level of controllability of these systems.
A neutron interferometer experiment which clearly demonstrates the violation of a Bell-like inequality is reported. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single particle. The total wave function of spin-1/2 neutron is described in a tensor product Hilbert space. Appropriate combinations of the direction of spin analysis and the position of the phase shifter allow experimental verification of the violation of a Bell-like inequality. Manipulation of the wave function in one Hilbert space influences the result of the measurement in the other Hilbert space: manipulation without touch! The violation of the Bell-like inequality is discussed in terms of quantum contextuality and an entanglement-induced correlation.
Neutron optical experiments are presented, which exhibit quantum contextual phenomena. Entanglement is achieved not between particles, but between degrees of freedom, 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. Our experiments manifest the fact that manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space: manipulation without touch! Next, we report another experiment which exhibits other peculiarity of quantum contextuality, e.g., originally intended to show a Kochen‐Specker‐like phenomenon. We have introduced inequalities for quantitative analysis of the experiments. The value obtained in the experiments clearly showed violations of prediction by non‐contextual theory. Finally, we have accomplished a tomographic determination of entangled quantum state in single‐neutrons. There, characteristics of the Bell‐sate are confirmed: four poles for the real part of the density matrix are clearly seen.
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