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arXiv:1902.11092 · Physical Review A

Macroscopicity of quantum mechanical superposition tests via hypothesis falsification

Björn Schrinski, Stefan Nimmrichter, Benjamin A. Stickler, Klaus Hornberger

Published Sep 16, 2019• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.100.032111

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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.
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.
Abstract Identifying which quantum states qualify as macroscopic superpositions remains a fundamental challenge in quantum physics, as no universally accepted operational criterion currently exists. In this work we introduce a dynamical criterion for macroscopic quantum superposition based on the continuous-measurement-based measure of quantum superposition together with the principle of macrorealism. The key idea is to characterize macroscopicity through the rate of purity decay of the quantum state under continuous monitoring, which quantifies the susceptibility of quantum coherence to classicalizing mechanisms. Two classes of macrorealistic dynamics are considered: environmental decoherence described by a Lindblad master equation (class A) and objective collapse dynamics in the continuous spontaneous localization model (class B). Applying this framework to an optomechanical oscillator, we show that the emergence of macroscopic superposition depends on the competition between measurement-induced decoherence and the macrorealistic mechanism. In class A the relevant contributions increase with excitation number, whereas in class B large excitation numbers can suppress macroscopicity. Unlike many existing macroscopicity measures based solely on phase-space structure or decoherence times, the present criterion directly relates macroscopicity to experimentally accessible parameters in continuous quantum measurement.
Macroscopic realism is the name for a class of modifications to quantum theory that allow macroscopic objects to be described in a measurement-independent manner, while largely preserving a fully quantum mechanical description of the microscopic world. Objective collapse theories are examples which aim to solve the quantum measurement problem through modified dynamical laws. Whether such theories describe nature, however, is not known. Here we describe and implement an experimental protocol capable of constraining theories of this class, that is more noise tolerant and conceptually transparent than the original Leggett-Garg test. We implement the protocol in a superconducting flux qubit, and rule out (by ∼84 s.d.) those theories which would deny coherent superpositions of 170 nA currents over a ∼10 ns timescale. Further, we address the 'clumsiness loophole' by determining classical disturbance with control experiments. Our results constitute strong evidence for the superposition of states of nontrivial macroscopic distinctness.
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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.