Mechanical displacements of a nanoelectromechanical system (NEMS) shift the electron trajectories and hence perturb phase coherent charge transport through the device. We show theoretically that in the presence of a magnetic feld such quantum-coherent displacements may give rise to an Aharonov-Bohm-type of effect. In particular, we demonstrate that quantum vibrations of a suspended carbon nanotube result in a positive nanotube magnetoresistance, which decreases slowly with the increase of temperature. This effect may enable one to detect quantum displacement fluctuations of a nanomechanical device.PACS numbers: 73.40Gk Following the ubiquitous trend of downsizing devices, micromechanical systems (MEMS) are today evolving into nanoelectromechanical systems (NEMS) rapidly approaching the limits set by the laws of quantum mechanics [1]. The ultimate potential for nanomechanical devices is governed by the ability to detect the NEMS motional response to various external stimuli. In the quantum regime of operation optical and other sensing methods used in MEMS are not practical and one has turned instead to various mesocopic sensing devices. Much work, including fundamental research, still needs to be done. For example, even though one has recently been able to detect flexural vibrations of a SiN beam resonator with the amazing sensitivity of 10 −13 m using a radiofrequency single-electron transistor [2], this is still about 6 times the quantum limit set by the amplitude of the zero-point oscillations of the beam.In this Letter we propose a different approach to sensing ultrasmall quantum vibrations of a beam -we have a suspended carbon nanotube in mind -and show that coherent tube vibrations can induce an effectively multiconnected electron path through the tube. Through an Aharonov-Bohm-type effect this in turn gives rise to a negative magneto-conductance that can be detected. We propose that this is but one example of how employing quantum coherence in both the electronic and mechanical degrees of freedom may lead to new functionality and novel applications.Fundamental research on NEMS in the quantum coherent regime can profit from analogies with mesoscopic phenomena in confined structures, where the conductance may depend on quantum interference between electron waves. It is, e.g., well known that the conductance of a mesoscopic sample changes if a single impurity is displaced a small distance and that varying a magnetic field leaves a sample-specific "magnetic fingerprint" conductance pattern. We will show that a similar effect can be achieved by the mechanical displacement corresponding to quantum vibrations of a suspended carbon nanotube in the presence of a magnetic field. To this end, consider first the structure shown in Fig. 1(b). Here a beam of electrons can pass through two openings in an otherwise opaque screen. Interference between the quantum amplitudes for going through one or the other of the two holes will determine the probability for electrons to hit the detector. Obviously no such interferenc...