Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown by Bell [1] and Kochen-Specker [2], quantum mechanics portrays a picture of the world in which reality loses its objectivity and is in fact created by observation. Quantum mechanics predicts phenomena which cannot be explained by any theory with objective realism, although our everyday experience supports the hypothesis that macroscopic objects, despite being made of quantum particles, exist independently of the act of observation; in this paper we identify this behavior as classical. Here we show that this seemingly obvious classical behavior of the macroscopic world cannot be experimentally tested and belongs to the realm of ontology similar to the dispute on the interpretations of quantum mechanics [3,4]. For small systems such as a single photon [5] or a pair [6], it has been experimentally proven that a classical description cannot be sustained. Recently, there have also been experiments that claim to have demonstrated quantum behavior of relatively large objects such as interference of fullerenes [7], the violation of Leggett-Garg inequality in Josephson junction [8], and interference between two condensed clouds of atoms [9], which suggest that there is no limit to the size of the system on which the quantum-versus-classical question can be tested. These behaviors, however, are not sufficient to refute classical description in the sense of objective reality. Our findings show that once we reach the regime where an Avogadro number of particles is present, the quantum-versus-classical question cannot be answered experimentally.
We investigate how to experimentally detect a recently proposed measure to quantify macroscopic quantum superpositions [Phys. Rev. Lett. 106, 220401 (2011)], namely, "macroscopic quantumness" $\mathcal{I}$. 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.
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 Schrödinger'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 quantu…
We present a review and discussions on characterizations and quantifications of macroscopic quantum states as well as their implementations and applications in optical systems. We compare and criticize different measures proposed to define and quantify macroscopic quantum superpositions and extend such comparisons to several types of optical quantum states actively considered for experimental implementations within recent research topics.
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 domain from weak to strong optomechanical coupling, illustrating how measurements performed over the cavity field that drives the dynamics of a mechanical system are able to steer the latter towards 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 …
The issues, raised in arXiv:0809.011, concerning the relevance of the von Neumann theorem for the single-system's quantumness test proposed in arXiv:0704.1962 and performed for the case of single photon polarization in arXiv:0804.1646, and the usefulness of Bell's inequality for testing the idea of macroscopic quantum systems are discussed in some details. Finally, the proper quantum mechanical description of the experiment with polarized photon beams is presented.
General wisdom tells us that if two quantum states are ``macroscopically distinguishable'' then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum nature of a superposition of two states that can be distinguished without microscopic accuracy. First, we quantify the distinguishability of any given pair of quantum states with measurement devices lacking microscopic accuracy, i.e. measurements suffering from limited resolution or limited sensitivity. Next, we quantify the required stability that have to be…
It is commonly expected that quantum theory is universal, in that it describes the world at all scales. Yet, quantum effects at the macroscopic scale continue to elude our experimental observation. This fact is commonly attributed to decoherence processes affecting systems of sufficiently large number of constituent subsystems leading to an effective macro-scale beyond which a quantum description of the whole system becomes superfluous. Here, we show both theoretically and experimentally that the existence of such a scale is unjustifiable from an information-theoretic perspective. We introduce…
Equilibration and the eigenstate thermalization hypothesis as limits to observing macroscopic quantum superpositions
Escola Politécnica de Pernambuco, Universidade de Pernambuco（伯南布哥联邦大学应用理工学院）；Universidade Estadual de Santa Cruz（圣克鲁斯州立大学）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
With the slow but constant progress in the coherent control of quantum systems, it is now possible to create large quantum superpositions. There has therefore been an increased interest in quantifying any claims of macroscopicity. We attempt here to motivate three criteria which we believe should enter in the assessment of macroscopic quantumness: The number of quantum fluctuation photons, the purity of the states, and the ease with which the branches making up the state can be distinguished.
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability distributions. The only possible criteria of quantum behaviour are statistical ones. Therefore I propose to consider any system which produces quantum statistics as quantum ("quantumlike"). A possible test is based on the interference of probabilities. I was mainly interested in using such an approach to "quantumness" to extend the domain of applications of quantum math…
There exists an increasing evidence supporting the picture of the Josephson junction (JJ) as a "macroscopic quantum system". On the other hand the interpretation of experimental data strongly depends on the assumed theoretical model. We analyse the possible states of a Cooper pair box ("charge qubit") for the two types of models : two-mode Bose-Hubbard model with its large $N$ aproximations and the many-body description within the mean-field approximation (Gross-Pitaevski equation). While the first class of models supports the picture of JJ being a quantum subsystem of a single degree of freed…
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.
Quantum entanglement between two or more bipartite entities is a core concept in quantum information areas limited to microscopic regimes directly governed by Heisenberg uncertainty principle via quantum superposition, resulting in nondeterministic and probabilistic quantum features. Such quantum features cannot be generated by classical means. Here, a pure classical method of on-demand entangled light-pair generation is presented in a macroscopic regime via basis randomness. This conflicting idea of conventional quantum mechanics invokes a fundamental question about both classicality and quan…
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, we critically analyze and discuss measures aiming to quantify various aspects of macroscopic quantumness. We survey recent results on the difficulties and prospects to create, maintain and detect macroscopic quantum states. The role of macroscopic quantum states in foundational questions as well as practical applications is ou…
Nonclassical phenomena of quantum mechanics such as anticorrelation and photonic de Broglie waves (PBWs) have been recently understood as a special case of coherence optics with a particular phase relation between orthogonal bases composing a classical system. Such a macroscopic understanding of nonclassical features has also been confirmed experimentally for a coherence version of PBWs in a doubly-coupled Mach-Zehnder interferometer (MZI). Here, a multi-coupled MZI system is analyzed and discussed to obtain a general understanding of the nonclassical feature using tensor products of binary ba…
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 multiple superposition states. 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 num…
Franson-type nonlocal quantum correlation based on the particle nature of quantum mechanics has been intensively studied for both fundamental physics and potential applications of quantum key distribution between remotely separated parties over the last several decades. Recently, a coherence theory of deterministic quantum features has been applied for Franson-type nonlocal correlation [arXiv:2102.06463] to understand its quantumness in a purely classical manner, where the resulting features are deterministic and macroscopic. Here, nearly sub-Poisson distributed coherent photon pairs obtained …
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to …
Macroscopic quantum phenomena refer to quantum features in objects of `large' sizes, systems with many components or degrees of freedom, organized in ways where they can be identified as macroscopic objects. This emerging field is ushered in by several categories of definitive experiments in superconductivity, electromechanical systems, Bose-Einstein condensates and others. Yet this new field which is rich in open issues at the foundation of quantum and statistical physics remains little explored theoretically [1]. This talk summarizes our thoughts on attempting a systematic investigation into…
We study the loss of quantumness caused by time dilation [1] for a Schrödinger cat state. We give a holistic view of the quantum to classical transition by comparing the dynamics of several nonclassicality indicators, such as the Wigner function interference fringe, the negativity of the Wigner function, the nonclassical depth, the Vogel criterion and the Klyshko criterion. Our results show that only two of these indicators depend critically on the size of the cat, namely on how macroscopic the superposition is. Finally we compare the gravitation-induced decoherence times to the typical decohe…
Quantum mechanics predicts superposition of position states even for macroscopic objects. Recently, the use of a quasi-freely suspended mirror combined with laser was proposed to prepare such states, by Müller-Ebhardt et al. [Phys.Rev.Lett.100, 013601 (2008)]. One of the key milestones towards this goal is the preparation of the mechanical oscillator mainly driven by quantum back-action, which identifies the connection between the object and quantumness of the light. Here, we describe development of a suspended 5-mg mirror driven by quantum back-action larger than thermal fluctuating force by …
How Quantum Contextuality disappears in the Classical Limit
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas（坎皮纳斯州立大学数学、统计与科学计算研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all …
We demonstrate, that artificial neural networks (ANN) can be trained to emulate single or multiple basic quantum operations. In order to realize a quantum state, we implement a novel "quantumness gate" that maps an arbitrary matrix to the real representation of a positive hermitean normalized density matrix. We train the CNOT gate, the Hadamard gate and a rotation in Hilbert space as basic building blocks for processing the quantum density matrices of two entangled qubits. During the training process the neural networks learn to represent the complex structure, the hermiticity, the normalizati…
We analyse the nature of spontaneous symmetry breaking in complex quantum systems by investigating the long-standing conjecture that the maximally symmetry-breaking quantum ground states are the most classical ones corresponding to a globally ordered phase. We make this argument quantitatively precise by comparing different local and global indicators of classicality and quantumness, respectively in symmetry-breaking and symmetry-preserving quantum ground states. We first discuss how naively comparing local, pairwise entanglement and discord apparently leads to the opposite conclusion. Indeed,…
