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Assessing the macroscopicity of quantum mechanical superposition tests via hypothesis falsification

Björn Schrinski

Published Oct 17, 2019• 1 citation

Abstract

In this thesis I present a universal scheme to assess the macroscopicity of experimentally fabricated quantum superposition states based on the degree to which they probe the boundaries of quantum mechanics. The measure relies on the falsification of the weakest macrorealist modifications of quantum mechanics; it treats all experiments in an equal manner, regardless the actual form and size of the empirical data, using an uninformative approach to Bayesian inference. The versatility of this scheme is illustrated by applying it on state-of-the-art quantum tests where the study of minimal modifications of quantum mechanics often coincides with the examination of conventional decoherence effects. Finally, the environmental impact on orientational degrees of freedom, leading to diffusion, friction, and thermalization, are described analytically. Together with the formulation of minimal modifications of quantum mechanics applied to orientational degrees of freedom this paves the way for a thorough description of experiments with levitated nanorotors and the assessment of the respective macroscopicities.

DOI: 10.17185/duepublico/70585

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We establish an objective scheme to determine the macroscopicity of quantum superposition tests with mechanical degrees of freedom. It is based on the Bayesian hypothesis falsification of a class of macrorealist modifications of quantum theory, such as the model of continuous spontaneous localization. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum mechanical test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation and read-out of nanomechanical oscillators.

We address the challenge of certifying quantum behavior with single macroscopic massive particles, subject to decoherence and finite data. We propose a hypothesis-testing framework that distinguishes between classical and quantum mechanics based on position measurements. While interference pattern visibility in single-particle quantum superposition experiments has been commonly used as a sufficient criterion to falsify classical mechanics, we show that, from a hypothesis-testing perspective, it is neither necessary nor efficient. Focusing on recent proposals to prepare macroscopic superposition states of levitated nanoparticles, we show that the likelihood ratio test—which leverages differences across the entire probability distribution—provides an exponential reduction in measurements needed to reach a given confidence level. These results generalize to a broad class of quantum states, and offer a principled, efficient method to falsify classical mechanics in interference experiments, relaxing the experimental constraints faced by current efforts to test quantum mechanics at the macroscopic scale.

Whether quantum physics is universally valid is an open question with far-reaching implications. Intense research is therefore invested into testing the quantum superposition principle with ever heavier and more complex objects. Here we propose a radically new, experimentally viable route towards studies at the quantum-to-classical borderline by probing the orientational quantum revivals of a nanoscale rigid rotor. The proposed interference experiment testifies a macroscopic superposition of all possible orientations. It requires no diffraction grating, uses only a single levitated particle, and works with moderate motional temperatures under realistic environmental conditions. The first exploitation of quantum rotations of a massive object opens the door to new tests of quantum physics with submicron particles and to quantum gyroscopic torque sensors, holding the potential to improve state-of-the-art devices by many orders of magnitude.

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