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arXiv:1505.03792 · Physical Review A

General framework for quantum macroscopicity in terms of coherence

Benjamin Yadin, Vlatko Vedral

Published Feb 26, 2016• 114 citations
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Abstract

We propose a universal language to assess macroscopic quantumness in terms of coherence, with a set of conditions that should be satisfied by any measure of macroscopic coherence. We link the framework to the resource theory of asymmetry. We show that the quantum Fisher information gives a good measure of macroscopic coherence, enabling a rigorous justification of a previously proposed measure of macroscopicity. This picture lets us draw connections between different measures of macroscopicity and evaluate them; we show that another widely studied measure fails one of our criteria.

DOI
10.1103/physreva.93.022122

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We propose a universal language to assess macroscopic quantumness in terms of coherence, with a set of conditions that should be satisfied by any measure of macroscopic coherence. We link the framework to the resource theory of asymmetry. We show that the quantum Fisher information gives a good measure of macroscopic coherence, enabling a rigorous justification of a previously proposed measure of macroscopicity. This picture lets us draw connections between different measures of macroscopicity and evaluate them; we show that another widely studied measure fails one of our criteria.
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We propose a novel approach to quantify quantum coherence which, contrary to the previous ones, does not rely on resource theory but rather on ontological considerations. In this framework, coherence is understood as the ability of a quantum system’s statistics to deviate from the total probability formula. After motivating the importance of the total probability formula in quantum foundations, we propose a new set of axioms that a measure of coherence should satisfy, and show that it defines a class of measures different from the main previous proposal. Finally, we prove a general result about the dependence of the [Formula: see text]-coherence norm on the basis of interest, and show that it is well approximated by the square root of the purity in most bases.
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of 10 5 to 10 7 atoms in recent mechanical superposition states.
The notion of the macroscopic in fundamental quantum theory is analyzed. After a brief summary of use of the term macroscopic, its use in quantum theory is compared with its previous use elsewhere. Next, the connections specifically to the Copenhagen interpretation of quantum mechanics and quantum measurement theory more generally, where this term first began to deviate from previous uses, are explained and exhibited through a number of examples. Then, recent attempts to define accurately and quantitatively the extent of being macroscopic, that is, macroscopicity are discussed and their implications considered. This is done most particularly in the realm of quantum optics, where it differs most from previous uses and has recently been of considerable interest. Finally, with the benefit of this analysis, recommendations are made regarding future use of the notion of the macroscopic in fundamental physics.
We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining conditions for measures of coherence we identify classes of functionals that satisfy these conditions and other, at first glance natural quantities, that do not qualify as coherence measures. We conclude with an outline of the questions that remain to be answered to complete the theory of coherence as a resource.