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.

We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)10.1103/PhysRevLett.100.130404], a Bell-like state was generated, and three expectation values were determined. The observed violation 2.291 +/- 0.008 not less, dbl equals1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.

From its very beginning, quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schrödinger cats and quantum non-locality. Another paradoxical phenomenon found within the framework of quantum mechanics is the ‘quantum Cheshire Cat’: if a quantum system is subject to a certain pre- and postselection, it can behave as if a particle and its property are spatially separated. It has been suggested to employ weak measurements in order to explore the Cheshire Cat’s nature. Here we report an experiment in which we send neutrons through a perfect silicon crystal interferometer and perform weak measurements to probe the location of the particle and its magnetic moment. The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other.

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.

A novel method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently Vallone and Dequal showed theoretically that weak measurements are not a necessary condition to determine the weak value [Phys. Rev. Lett. 116, 040502 (2016)]. Here we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system's quantum state was characterized via direct measurements using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones. Our results are not limited to neutron interferometry, but can be used in a wide range of quantum systems. [17,18]. One can also take a pragmatic approach and simply treat the weak value as a complex number that is accessible by experiment, as done in direct state characterization [19,20] to determine complex quantum state probability amplitudes in a particular basis. The weak value of observable of a quantum system is given bywhere |ψ i and |ψ f are the initial (preselected) and final (postselected) system states respectively. To determine  w a probe system, which serves as a measurement apparatus, has to be coupled to the observed system, leading to an entanglement between them. In the usual weak measurement approach only minimally disturbing interactions, between the quantum system and the measurement apparatus are regarded. However, as was recently pointed out theoretically [21,22], the weakness of the interaction is not a necessary condition to obtain the weak value. Furthermore it was shown that strong measurements give a better direct measurement of the quantum wave function using the weak value.