One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

/pdf/the-classical-quantum-boundary-for-correlations-discord-and-3rixt19msw.pdf

The classical-quantum boundary for correlations: Discord and related measures

Multiphoton interference reveals strictly nonclassical phenomena. Its applications range from fundamental tests of quantum mechanics to photonic quantum information processing, where a significant fraction of key experiments achieved so far comes from multiphoton state manipulation. The progress, both theoretical and experimental, of this rapidly advancing research is reviewed. The emphasis is given to the creation of photonic entanglement of various forms, tests of the completeness of quantum mechanics (in particular, violations of local realism), quantum information protocols for quantum communication (e.g., quantum teleportation, entanglement purification, and quantum repeater), and quantum computation with linear optics. The scope of the review is limited to ``few-photon'' phenomena involving measurements of discrete observables.

/pdf/multiphoton-entanglement-and-interferometry-36qb24ejfd.pdf

Multiphoton entanglement and interferometry

A vision has formed in recent years of the components necessary for a large-scale quantum network. Single trapped atoms can serve as the nodes of this network, with the links established by flying photons that are coupled to the atoms using optical resonators. This review describes progress towards the goal of multinode networks using the current generation of experiments, which have achieved unprecedented levels of atomic qubit control and light-matter coupling efficiencies.

Cavity-based quantum networks with single atoms and optical photons

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.

An introduction to quantum machine learning

Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research-quantum information versus machine learning (ML) and artificial intelligence (AI)-have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our 'big data' world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement-exploring what ML/AI can do for quantum physics and vice versa-researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.

https://iopscience.iop.org/article/10.1088/1361-6633/aab406/pdf

Machine learning & artificial intelligence in the quantum domain: a review of recent progress.

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation exist. These models have been shown to be formally equivalent, but their underlying elementary concepts and the requirements for their practical realization can differ significantly. A particularly exciting paradigm is that of measurement-based quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state. We review recent developments in measurement-based quantum computation with a view to both fundamental and practical issues, in particular the power of quantum computation, the protection against noise (fault tolerance) and steps towards experimental realization. Finally, we highlight a number of connections between this field and other branches of physics and mathematics. So-called one-way schemes have emerged as a powerful model to describe and implement quantum computation. This article reviews recent progress, highlights connections to other areas of physics and discusses future directions.

Measurement-based quantum computation

Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster-state model, and it was hence believed that with this approach, many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as "computationally universal" states-i.e., they allow one to efficiently reproduce the classical output of each quantum computation-whereas the cluster states are universal in a stronger sense since they are "universal state preparators." Here, we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.

pdf/quantum-computation-in-correlation-space-and-extremal-3x1lgldpih.pdf

Quantum Computation in Correlation Space and Extremal Entanglement

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Measurement-based quantum computation

Quantum Computation in Correlation Space and Extremal Entanglement