New uncertainty relations and wave-particle duality studied with neutrons

Neutron interference experiments have long been serving us as an almost ideal strategy to study foundations of quantum mechanics with matter-waves. Above all, interferometric experiments using massive particles, i.e. neutrons, enable investigations of fundamental phenomena in quantum mechanics with beam separation in the order of several centimeters, i.e., actually quantum interference experiments on the macroscopic scale. This technique allowed us many text-book experiments of quantum physics such as demonstrations of 4 spinor symmetry of 1/2-spin, spin superposition, gravitationally induced phase and non-inertial motional effects. Moreover, utilizing interference effect between two spin eigenstates, an alternative method using neutron polarimeters has turned out to be another useful tool for investigations of quantum mechanical two-level system. This apparatus is used for quantum-mechanical measurements, particularly in cases where high stability and efficiency are called for. In this project, following our recent successful investigations and exploiting the technique developed in previous experiments, we proceed studies of uncertainty relations in various forms with neutrons matter-waves. Furthermore, interferometer experiments enable to extend the concept of uncertainty relation and give new insights of wave-particle duality. Three major research targets are set: (i)Implementation of incompatible spin measurements suitable for the study of further-developed and tight error-disturbance uncertainty relation by Ozawa and Branciard. (ii) Studies of information-theoretic uncertainty relation in a form with binary entropy function, where error correction operation is a key issue of the studies from the theoretical and experimental points of view. (iii) Studies of extended uncertainty relation for path/distinguishability and wave/fringe-amplitude in double-slit situations, where new insights concerning the wave-particle duality are anticipated. In the previous project Double, triple and quadruple entanglement of neutrons (July 2009 ~ October 2013), we accomplished the experimental implementation of a multi-partite entangled state in neutron interferometers and polarimeters. In addition, a neutron polarimetric experiment confirmed the violation of the old error-disturbance uncertainty relation by Heisenberg and the validity a new universally valid formation. It is worth noting here that this experiment stimulated the studies of uncertainty relation theoretically and experimentally. On the basis of these achievements, we believe that we can proceed further experimental studies of new uncertainty relations, namely by using neutrons matter-waves. Moreover, we hope that studies with neutron interferometers enable to extend the uncertainty relation for double-slit situations and bring new insight of wave-particle duality. In all cases experimental investigation will have priority and theoretical support will be provided from collaborations with other groups, in Japan, Australia, and worldwide. The aim of the project is to contribute also to the impressive progress of quantum optics, quantum information/communication technology and quantum metrology by the use of the specific properties of neutrons as an elementary matter wave system. 1

From the very start, optical experiments, in particular with matter-wave interferometers, have been serving as a powerful technique for the investigation of foundations of quantum mechanics; electrons, neutrons, atoms, and even molecules are used in many experiments. Lots of exemplary experiments of quantum physics have been performed with this technique and earned a wide reputation. Neutron physics group at the Atominstitut, TU-Wien has been performing such an optical experiment with neutrons for many decades; we have accomplished advanced experiments, for instance, studying peculiarities of quantum mechanics and testing alternative quantum theories. Recently, we reported a polarimeter experiment with neutrons that reveal the invalidity of the uncertainty relations, originally formulated by Heisenberg in 1927. The present project aims to investigate all aspects of uncertainty relations, from a quantum-measurement theoretical as well as an informational point of view. As was used in the first experimental test of Heisenberg's uncertainty relations, polarimeter setup for neutrons serves as the fundamental strategy, where quantum measurements and manipulations for neutrons' -spin are performed with high accuracy. We started by reporting an experimental test of the entropic noise-disturbance uncertainty relation. Noise and disturbance, defined based on the information-theoretic consideration, are determined for non-commuting projective measurements; obtained results confirmed the tight noise-disturbance uncertainty relation. This study was later expanded for cases of more general quantum measurements, leaving the limitations of the projective measurements. A tradeoff between the noises for two arbitrary spin measurements is confirmed; we observed that the tradeoff is only saturated by general quantum measurements as predicted by the theory. Furthermore, residual error and disturbance for general mixed input-state input was investigated in another neutron polarimeter experiment; a new bound is experimentally confirmed, which is the consequence of the residual uncertainty for the mixed input-states. In parallel, spin-rotation coupling was studied, in particular in neutron interferometer setup, where a phase shift of purely quantum-mechanical origin was confirmed. Note that all experiments mentioned above are feasible only after appropriate development of some important optical elements used in the neutron polarimeter and interferometer experiments. In total, the project offered significant advance of the studies of uncertainty relations with neutron's matter-waves optical setup. Noteworthy successes are achieved in studying uncertainty relations for quantum measurements in terms of root-mean-square as well as entropy; the former is based on the quantum-measurement theoretical and the latter is on the information-theoretic considerations.