The timeline of the expansion rate ultimately defines the interplay between high-energy physics, astrophysics and cosmology. The guiding theme of this topical review is provided by the scrutiny of the early history of the space–time curvature through the diffuse backgrounds of gravitational radiation that are sensitive to all the stages of the evolution of the plasma. Due to their broad spectrum (extending from the aHz region to the THz domain) they bridge the macroworld described by general relativity and the microworld of the fundamental constituents of matter. It is argued that during the next score year the analysis of the relic gravitons may infirm or confirm the current paradigm where a radiation plasma is assumed to dominate the whole post-inflationary epoch. The role of high frequency and ultra-high frequency signals between the MHz and the THz is emphasized in the perspective of quantum sensing. The multiparticle final state of the relic gravitons and its macroscopic quantumness is also discussed with particular attention to the interplay between the entanglement entropy and the maximal frequency of the spectrum.

Macroscopic quantum effects play central roles in the appearance of\ninexplicable phenomena in low-temperature quantum many-body physics. Such\nmacroscopic quantumness is often evaluated using long-range entanglement, i.e.,\nentanglement in the macroscopic length scale. The long-range entanglement not\nonly characterizes the novel quantum phases but also serves as a critical\nresource for quantum computation. Thus, the problem that arises is under which\nconditions can the long-range entanglement be stable even at room temperatures.\nHere, we show that bi-partite long-range entanglement is unstable at arbitrary\ntemperatures and exponentially decays with distance. Our theorem provides a\nno-go theorem on the existence of the long-range entanglement. The obtained\nresults are consistent with the existing observations that long-range\nentanglement at non-zero temperatures can exist in topologically ordered\nphases, where tripartite correlations are dominant. In the derivation of our\nresult, we introduce a quantum correlation defined by the convex roof of the\nstandard correlation function. We establish an exponential clustering theorem\nfor generic quantum many-body systems for such a quantum correlation at\narbitrary temperatures, which yields our main result by relating quantum\ncorrelation to quantum entanglement. As a simple application of our analytical\ntechniques, we derived a general limit on the Wigner-Yanase-Dyson skew\ninformation and the quantum Fisher information, which will attract significant\nattention in the field of quantum metrology. Our work reveals novel general\naspects of low-temperature quantum physics and sheds light on the\ncharacterization of long-range entanglement.\n

One of the most elusive problems in quantum mechanics is the transition between classical and quantum physics. This problem can be traced back to the Schr\"{o}dinger's cat. A key element that lies at the center of this problem is the lack of a clear understanding and characterization of macroscopic quantum states. Our understanding of Macroscopic Quantumness relies on states such as the Greenberger-Horne-Zeilinger(GHZ) or the NOON state. Here we take a first principle approach to this problem. We start from coherence as the key quantity that captures the notion of quantumness and demand the quantumness to be collective and macroscopic. To this end, we introduce macroscopic coherence which is the coherence between macroscopically distinct quantum states. We construct a measure that quantifies how global and collective the coherence of the state is. Our work also provides a first-principle way to derive well-established states like the GHZ and the NOON state as the states that maximize our measure. This new approach paves the way towards a better understanding of the Quantum-to-Classical transition.

We address the macroscopic quantumness of the state of mechanical systems subjected to conditional protocols devised for state engineering in cavity optomechanics. We use a measure of macroscopicity based on phase-space methods. We cover the transition regime into strong single-photon coupling, illustrating how measurements performed over the cavity field that drives the dynamics of a mechanical system are able to steer the latter toward large quantum coherent states. The effect of losses is evaluated for the case of an open cavity and analyzed in terms of the features of the Wigner functions of the state of the mechanical system. We also address the case of engineered phonon-subtracted mechanical systems, in full open-system configuration, demonstrating the existence of optimal working points for the sake of mesoscopic quantumness. Our study is relevant for and applicable to a broad range of settings, from clamped to levitated mechanical systems.

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.16 MoreReceived 19 June 2017DOI:https://doi.org/10.1103/RevModPhys.90.025004© 2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum measurementsQuantum metrologyQuantum states of lightQuantum Information

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

We consider the characterization of quantum superposition states beyond the pattern ‘dead and alive’. We propose a measure that is applicable to superpositions of multiple macroscopically distinct states, superpositions with different weights as well as mixed states. The measure is based on the mutual information to characterize the distinguishability between the multiple branches of the superposition. This allows us to overcome limitations of previous proposals, and to bridge the gap between general measures for macroscopic quantumness and measures for Schrödinger-cat type superpositions. We discuss a number of relevant examples, provide an alternative definition using basis-dependent quantum discord and reveal connections to other proposals in the literature. Finally, we also show the connection between the size of quantum states as quantified by our measure and their vulnerability to noise.

Abstract We investigate the macroscopic quantumness of a set of stateswell approximating the important class of coherent state-encoded Schrödinger cat states. We do so by using two different quantifiers of macroscopic quantumness, finding consistency between the results arising from the two quantifiers, despite the different grounds upon which they are built.

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.

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.

Assessments of macroscopicity for quantum optical states

Macroscopicity in an optomechanical matter-wave interferometer