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arXiv:1205.3447 · Physical Review Letters

Macroscopicity of Mechanical Quantum Superposition States

Stefan Nimmrichter, Klaus Hornberger

Published Apr 18, 2013• 202 citations
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Abstract

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.
DOI
10.1103/physrevlett.110.160403

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For evaluating the macroscopicity of superposition states in classic mechanical systems, we suggest an objective measure that is accessible through experimentation. One can measure the level of macroscopicity attained in various experiments based on the observable results of a minimum, macrorealist extension of modern classical mechanics. Numerous experiments have widely and independently supported general relativity. The interaction of the two theories has never been tested, though, as all tests that examined how gravity affects classic mechanical systems are compatible with Newtonian, non-relativistic gravity.
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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.
Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space.
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