Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data

Abstract

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.

7 pages, 3 figures

References in corpus (28)

• Encoding a qubit in an oscillator
• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature
• Testing the limits of quantum mechanical superpositions
• Real-time optimal quantum control of mechanical motion at room temperature
• Colloquium: Quantum interference of clusters and molecules
• Quantum control of a nanoparticle optically levitated in cryogenic free space
• Matter-wave interferometer for large molecules
• Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu
• Quantum Superposition of Massive Objects and Collapse Models
• Macroscopicity of Mechanical Quantum Superposition States
• Real-time single-molecule imaging of quantum interference
• Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle
• Wigner function negativity and contextuality in quantum computation on rebits
• Optical cold damping of neutral nanoparticles near the ground state in an optical lattice
• Two-dimensional quantum motion of a levitated nanosphere
• Coherent Inflation for Large Quantum Superpositions of Microspheres
• Ultra-high quality factor of a levitated nanomechanical oscillator
• Macroscopic Quantum Superpositions via Dynamics in a Wide Double-Well Potential
• Fast Quantum Interference of a Nanoparticle via Optical Potential Control
• Prediction and retrodiction with continuously monitored Gaussian states
• Macroscopicity of quantum mechanical superposition tests via hypothesis falsification
• Quantum-classical hypothesis tests in macroscopic matter-wave interferometry
• Cubic nonlinear squeezing and its decoherence
• Testing quantum mechanics: a statistical approach
• Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials
• Quantum retrodiction in Gaussian systems and applications in optomechanics
• Nonlinear Phase Gates as Airy Transforms of the Wigner Function