The author of the comment [1] claimed that the experimental results for a universally valid uncertainty relation cannot be recognized to establish a violation of the Heisenberg-type uncertainty relation. However, after careful examination of the author's argument, we regard the author's argument to be on an improper basis, thus disagree with his opinion. Hereby, we provide arguments to disprove his objection.According to his statement "To insist the violation of the Heisenbergtype uncertainty relation, ǫ(Q) = 0 or η(P ) = 0, one has to prove | [N (Q), D(P )] | = 0," he appears to formulate the violation to be the case where ǫ(Q) = 0 or η(P ) = 0. However, in our paper the violation is taken to be the cases where the relation ǫ(A)η(B) ≥ 1 2 | [A, B] | does not hold, and we observed the violation for all the parameter values of φ actually tested.The author conclude the comments by writing "In conclusion, the experimental set-up of ref.[2] is not satisfied the necessary condition to be true for the UVUR proved by Ozawa in [3,4], because the neutron spin measurement ("projective measurement" as well) does not have the unitary operator to defined the equal-time commutation relation".In contrast to what the author claimed, the projective measurement is defined by a family of projection operators M m , instead of a unitary operator U , and the root-mean-square error is defined by equation (5) in Ref.[2] using the projection operators M m , instead of using the unitary operator U . It is well-known that if the measurement is defined by a unitary operator U , then the definition of the root-mean-square error using the unitary operator U and the definition (5) in Ref.[2] using only projection operators M m are equivalent. A detailed account on those equivalences between definitions are given in [M. Ozawa, Uncertainty relations for noise and disturbance in generalized quantum measurements, Ann. Phys. (N.Y.) 311, 350-416 (2004)]. Thus, the author's criticism based on the absence of the unitary operator is also irrelevant.

Non-local correlations between spatially separated systems have been extensively discussed in the context of the Einstein, Podolsky and Rosen (EPR) paradox and Bell's inequalities. Many proposals and experiments designed to test hidden variable theories and the violation of Bell's inequalities have been reported; usually, these involve correlated photons, although recently an experiment was performed with (9)Be(+) ions. Nevertheless, it is of considerable interest to show that such correlations (arising from quantum mechanical entanglement) are not simply a peculiarity of photons. Here we measure correlations between two degrees of freedom (comprising spatial and spin components) of single neutrons; this removes the need for a source of entangled neutron pairs, which would present a considerable technical challenge. A Bell-like inequality is introduced to clarify the correlations that can arise between observables of otherwise independent degrees of freedom. We demonstrate the violation of this Bell-like inequality: our measured value is 2.051 +/- 0.019, clearly above the value of 2 predicted by classical hidden variable theories.

In its original formulation, Heisenberg's uncertainty principle dealt with the relationship between the error of a quantum measurement and the thereby induced disturbance on the measured object. Meanwhile, Heisenberg's heuristic arguments have turned out to be correct only for special cases. A new universally valid relation was derived by Ozawa in 2003. Here, we demonstrate that Ozawa's predictions hold for projective neutron-spin measurements. The experimental inaccessibility of error and disturbance claimed elsewhere has been overcome using a tomographic method. By a systematic variation of experimental parameters in the entire configuration space, the physical behavior of error and disturbance for projective spin-1 2 measurements is illustrated comprehensively. The violation of Heisenberg's original relation, as well as, the validity of Ozawa's relation become manifest. In addition, our results conclude that the widespread assumption of a reciprocal relation between error and disturbance is not valid in general.

No abstract

An experimental demonstration of quantum contextuality with neutrons is presented, which intended to exhibit a Kochen-Specker-like phenomenon. Since no perfect correlation is expected in practical experiments, inequalities are derived to distinguish quantitatively the obtained results from predictions by a noncontextual hidden variable theory. Experiments were accomplished with the use of a neutron interferometer combined with spinor manipulation devices. The results clearly violate the prediction of noncontextual theories.