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arXiv:1404.7256 · Journal of the Optical Society of America B

Detecting the degree of macroscopic quantumness using an overlap measurement

Hyunseok Jeong, Changsuk Noh, Seunglee Bae, Dimitris G. Angelakis, Timothy C. Ralph

Published Nov 17, 2014• 14 citations
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Abstract

We investigate how to experimentally detect a recently proposed measure to quantify macroscopic quantum superpositions [Phys. Rev. Lett.106, 220401 (2011)10.1103/PhysRevLett.106.220401PRLTAO0031-9007], namely, “macroscopic quantumness” I. Schemes based on overlap measurements for harmonic oscillator states and for qubit states are extensively investigated. Effects of detection inefficiency and coarse-graining are analyzed in order to assess feasibility of the schemes.

DOI
10.1364/josab.31.003057

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We investigate how to experimentally detect a recently proposed measure to quantify macroscopic quantum superpositions [Phys. Rev. Lett.106, 220401 (2011)10.1103/PhysRevLett.106.220401PRLTAO0031-9007], namely, “macroscopic quantumness” I. Schemes based on overlap measurements for harmonic oscillator states and for qubit states are extensively investigated. Effects of detection inefficiency and coarse-graining are analyzed in order to assess feasibility of the schemes.
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.
We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent results when considering certain states such as a product of microscopic superpositions. An inequality relation is proved that relates the Wigner–Yanase–Dyson skew information and the measurement disturbance, providing arguments as to why our approach is able to rule out such inconsistencies. We show that our measure can also quantify the fragility of a quantum state to a certain type of decoherence. Our work provides a general framework of quantifying macroscopic coherence from an operational point of view, based on the relationship between the precision of the measurement and disturbance of the quantum state.
Large-scale quantum effects have always played an important role in the foundations of quantum theory.With recent experimental progress and the aspiration for quantum enhanced applications, the interest in macroscopic quantum effects has been reinforced.In this review, measures aiming to quantify various aspects of macroscopic quantumness are critically analyzed and discussed.Recent results on the difficulties and prospects to create, maintain, and detect macroscopic quantum states are surveyed.The role of macroscopic quantum states in foundational questions as well as practical applications is outlined.Finally, past and ongoing experimental advances aiming to generate and observe macroscopic quantum states are presented.
It has recently been conjectured that detecting quantum effects such as superposition or entanglement for macroscopic systems always requires high measurement precision. Analyzing an apparent counter-example involving macroscopic coherent states and Kerr non-linearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary non-linear operations has to increase with the size of the system. This suggests a refined conjecture that either the {\it outcome precision} or the {\it control precision} of the measurements has to increase with system size.
We propose a criterion which defines whether a superposition of two photonic components is macroscopic. It is based on the ability to discriminate these components with a particular class of ``classical'' detectors, namely, a photon number measurement with a resolution coarse-grained by noise. We show how our criterion can be extended to a measure of the size of macroscopic superpositions by quantifying the amount of noise that can be tolerated and taking the distinctness of two Fock states differing by N photons as a reference. After applying our measure to several well-known examples, we demonstrate that the superpositions which meet our criterion are very sensitive to phase fluctuations. This suggests that quantifying the macroscopicity of a superposition state through the distinguishability of its components with ``classical'' detectors not only is a natural measure but also explains why it is difficult to observe superpositions at the macroscopic scale.