Experimental test of an entropic measurement uncertainty relation for arbitrary qubit observables

A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff relation between the noises for two arbitrary spin observables is demonstrated. The optimal bound of this tradeoff is experimentally obtained for various non-commuting spin observables. For some of these observables this lower bound can be reached with projective measurements, but we observe that, in other cases, the tradeoff is only saturated by general quantum measurements (i.e., positive-operator valued measures), as predicted theoretically.Comment: 6 pages, 3 figure

Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Three-Outcome Qubit Measurements

Information-theoretic uncertainty relations formulate the joint immeasurability of two non-commuting observables in terms of information entropies. The trade-off of the accuracy in the outcome of two successive measurements manifests in entropic noise-disturbance uncertainty relations. Recent theoretical analysis predicts that projective measurements are not optimal, with respect to the noise-disturbance trade-offs. Therefore the results in our previous letter [PRL 115, 030401 (2015)] are outperformed by general quantum measurements. Here, we experimentally test a tight information-theoretic measurement uncertainty relation for three-outcome positive-operator valued measures (POVM), using neutron spin-1/2 qubits. The obtained results violate the lower bound for projective measurements as theoretically predicted.Comment: 14 pages, 14 figure

Spin - Rotation Coupling Observed in Neutron Interferometry

Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree well with the predictions derived from the Pauli - Schr\"odinger equation

Observation of a quantum Cheshire Cat in a matter wave interferometer experiment

From its very beginning quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schr\"odinger cats and quantum non-locality. In the study of quantum measurement, a process involving pre- and postselection of quantum ensembles in combination with a weak interaction was found to yield unexpected outcomes. This scheme, usually referred to as "weak measurements", can not only be used as an amplification technique and for minimal disturbing measurements, but also for the exploration of quantum paradoxes. Recently the quantum Cheshire Cat has attracted attention: a quantum system can behave as if a particle and its property (e.g. its polarization) are spatially separated. Up to now most experiments studying weak measurements were done with photonic setups. To reveal the peculiarities of a quantum Cheshire Cat the use of non-zero mass particles is most appealing, since no classical description is possible. Here, we report an experiment using a neutron interferometer to create and observe a purely quantum mechanical Cheshire Cat. The experimental results suggest that the system behaves as if the neutrons went through one beam path, while their spin travelled along the other.Comment: 8 pages, 4 figures and 1 tabl

Residual error-disturbance uncertainties in successive spin-1/2 measurements tested in matter-wave optics

The indeterminacy inherent in quantum measurement is an outstanding character of quantum theory, which manifests itself typically in Heisenberg's error-disturbance uncertainty relation. In the last decade, Heisenberg's relation has been generalized to hold for completely general quantum measurements. Nevertheless, the strength of those relations has not been clarified yet for mixed quantum states. Recently, a new error-disturbance uncertainty relation (EDUR), stringent for generalized input states, has been introduced by one of the present authors. A neutron-optical experiment is carried out to investigate this new relation: it is tested whether error and disturbance of quantum measurements disappear or persist in mixing up the measured ensemble. Our results exhibit that measurement error and disturbance remain constant independent of the degree of mixture. The tightness of the new EDUR is confirmed, thereby validating the theoretical prediction

Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements

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.Comment: 17 pages, 13 figure

Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements

Information-theoretic definitions for noise and disturbance in quantum measurements were given in Phys. Rev. Lett. 112, 050401 (2014) and a state-independent noise-disturbance uncertainty relation was obtained. Here, we derive a tight noise-disturbance uncertainty relation for complementary qubit observables and carry out an experimental test. Successive projective measurements on the neutron's spin-1/2system, together with a correction procedure which reduces the disturbance, are performed. Our experimental results saturate the tight noise-disturbance uncertainty relation for qubits when an optimal correction procedure is applied.Comment: 5 pages, 5 figures plus Supplemental Material (5 pages, 4 figures

Additive Manufactured and Topology Optimized Permanent Magnet Spin-Rotator for Neutron Interferometry Applications

In neutron interferometric experiments using polarized neutrons coherent spin-rotation control is required. In this letter we present a new method for Larmor spin-rotation around an axis parallel to the outer guide field using topology optimized 3D printed magnets. The use of 3D printed magnets instead of magnetic coils avoids unwanted inductances and offers the advantage of no heat dissipation, which prevents potential loss in interferometric contrast due to temperature gradients in the interferometer. We use topology optimization to arrive at a design of the magnet geometry that is optimized for homogeneity of the magnetic action over the neutron beam profile and adjustability by varying the distance between the 3D printed magnets. We verify the performance in polarimetric and interferometric neutron experiments.Comment: 8 pages, 12 figure