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The Kochen-Specker theorem theoretically shows evidence of the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments by using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement in a single neutron system. Here entanglement is achieved not between different particles, but between degrees of freedom, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality of the Kochen-Specker theorem. The observed value of (2.291 +/- 0.008), which is above the threshold of 1, clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories., Comment: 5 pages, 3 figures

We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated the spin, path, and energy degrees of freedom in a single neutron system. The GHZ-like state was analyzed with an inequality derived by Mermin: we determined the four expectation values and finally obtained M = 2.558 +/- 0.004 > 2, which exhibits a clear violation of the noncontextual assumption and confirms quantum contextuality., Comment: 4 pages, 2figures

We show that an experimental demonstration of quantum contextuality using 2 degrees of freedom of single neutrons based on a violation of an inequality derived from the Peres-Mermin proof of the Kochen-Specker theorem would be more conclusive than those obtained from previous experiments involving pairs of ions [M. A. Rowe et al., Nature (London) 409, 791 (2001)] and single neutron [Y. Hasegawa et al., Nature (London) 425, 45 (2003)] based on violations of Clauser-Horne-Shimony-Holt-like inequalities., Comment: REVTeX4, 4 pages, 1 figure

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere., Comment: 4 pages, revtex4

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors [Hasegawa et al., PRA 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism [Wagh, PRA 59, 1715 (1999)]. The extension to non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment., Comment: presented at the Int. Conference on Precision Measurements with Slow Neutrons, April 2004, NIST, Gaithersburg, US

We report a single-neutron optical experiment to demonstrate the violation of a Bell-like inequality. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single-particle. The spin-{\small 1/2} property of neutrons are utilized. The total wave function of the neutron is described in a tensor product Hilbert space. A Bell-like inequality is derived not by a non-locality but by a contextuality. Joint measurements of the spinor and the path properties lead to the violation of a Bell-like inequality. Manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space. A discussion is given on the quantum contextuality and an entanglement-induced correlation in our experiment., Comment: 10 pages, 3 figures. for the proceedings of CEWQO10 workshop

Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example the discrete Fourier estimation that actually coincides with the operational phase of Noh, Fouge`res and Mandel is obtained for continuous Gaussian signals with phase modulated mean.Since signals in quantum theory are discrete, a prediction different from that given by the Gaussian hypothesis should be obtained as the best fit assuming a discrete Poissonian statistics of the signal. Although the Gaussian estimation gives a satisfactory approximation for fitting the phase distribution of almost any state the optimal phase estimation offers in certain cases a measurable better performance. This has been demonstrated in neutron--optical experiment., Comment: 8 pages, 4 figures

The dynamics of a quantum system undergoing frequent "measurements", leading to the so-called quantum Zeno effect, is examined on the basis of a neutron-spin experiment recently proposed for its demonstration. When the spatial degrees of freedom are duely taken into account, neutron-reflection effects become very important and may lead to an evolution which is totally different from the ideal case., Comment: 26 pages, 6 figures

The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system., Comment: 9 pages, LaTeX, including 1 epsfigure, tar+gzip+uuencoded to appear in Phys. Lett. A