Quantum metrology with nonclassical states of atomic ensembles
TL;DR: In this article, the authors review and illustrate the theory and experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.
Abstract: Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well-developed techniques for trapping, controlling, and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold, and ultracold gases of neutral atoms. Moreover, atoms can strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.
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TL;DR: In this article, a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states was used to demonstrate the creation of "Schrodinger cat" states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits.
Abstract: Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of “Schrodinger cat” states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.
368 citations
TL;DR: In this paper, the authors summarize the properties and existing calculation techniques of quantum Fisher Information Matrix (QFIM) for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology.
Abstract: Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cram\'{e}r-Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.
308 citations
Harvard University1, University of Washington2, Humboldt University of Berlin3, Imperial College London4, University of Belgrade5, Istituto Nazionale di Fisica Nucleare6, Technical University of Berlin7, University of Bordeaux8, University of Oxford9, University of Valencia10, University of Strathclyde11, Rutherford Appleton Laboratory12, King's College London13, Foundation for Research & Technology – Hellas14, University of Birmingham15, University College London16, University of Liverpool17, National Physical Laboratory18, University of Nottingham19, University of Sussex20, Fermilab21, Northern Illinois University22, Peking University23, University of Pisa24, University of California, Riverside25, University of Nevada, Reno26, CERN27, University of Niš28, National Institute of Chemical Physics and Biophysics29, Beni-Suef University30, British University in Egypt31, Leibniz University of Hanover32, Paul Sabatier University33, University of Paris34, University of Cambridge35, Wayne State University36, Stanford University37, University of Bergen38, University of Amsterdam39, Northwestern University40, University of Bristol41, University of Warsaw42, University of Illinois at Urbana–Champaign43, Fayoum University44, University of Crete45, Queen's University Belfast46, Brandeis University47, University of Bologna48, Cochin University of Science and Technology49, German Aerospace Center50, University of Manchester51, University of Copenhagen52, University of Düsseldorf53, University of Vienna54, Florida State University55, University of Florence56, University of Illinois at Chicago57, University of Bremen58, University of Mainz59, Chinese Academy of Sciences60, University of Cincinnati61
TL;DR: The Atomic Experiment for Dark Matter and Gravity Exploration (AEDGE) as mentioned in this paper is a space experiment using cold atoms to search for ultra-light dark matter, and to detect gravitational waves in the frequency range between the most sensitive ranges of LISA and the terrestrial LIGO/Virgo/KAGRA/INDIGO experiments.
Abstract: We propose in this White Paper a concept for a space experiment using cold atoms to search for ultra-light dark matter, and to detect gravitational waves in the frequency range between the most sensitive ranges of LISA and the terrestrial LIGO/Virgo/KAGRA/INDIGO experiments. This interdisciplinary experiment, called Atomic Experiment for Dark Matter and Gravity Exploration (AEDGE), will also complement other planned searches for dark matter, and exploit synergies with other gravitational wave detectors. We give examples of the extended range of sensitivity to ultra-light dark matter offered by AEDGE, and how its gravitational-wave measurements could explore the assembly of super-massive black holes, first-order phase transitions in the early universe and cosmic strings. AEDGE will be based upon technologies now being developed for terrestrial experiments using cold atoms, and will benefit from the space experience obtained with, e.g., LISA and cold atom experiments in microgravity.
259 citations
01 Jan 2019
TL;DR: The most commonly used quantifiers of entanglement are discussed and the state-of-the-art detection and certification methods are surveyed, including their respective underlying assumptions, from both a theoretical and an experimental point of view.
Abstract: Entanglement is an important resource for quantum technologies. There are many ways quantum systems can be entangled, ranging from the two-qubit case to entanglement in high dimensions or between many parties. Consequently, many entanglement quantifiers and classifiers exist, corresponding to different operational paradigms and mathematical techniques. However, for most quantum systems, exactly quantifying the amount of entanglement is extremely demanding, if at all possible. Furthermore, it is difficult to experimentally control and measure complex quantum states. Therefore, there are various approaches to experimentally detect and certify entanglement when exact quantification is not an option. The applicability and performance of these methods strongly depend on the assumptions regarding the involved quantum states and measurements, in short, on the available prior information about the quantum system. In this Review, we discuss the most commonly used quantifiers of entanglement and survey the state-of-the-art detection and certification methods, including their respective underlying assumptions, from both a theoretical and an experimental point of view. Entanglement is often considered the defining feature separating classical physics from quantum physics and provides the basis for many quantum technologies. This Review discusses recent progress in the challenging task of conclusively proving that a physical system features entanglement, surveying detection and certification methods.
250 citations
01 Mar 2021
TL;DR: This Review describes the current state of the art in semiconductor charge and spin qubits based on gate-controlled semiconductor quantum dots, shallow dopants, and color centers in wide band gap materials.
Abstract: In the past decade, semiconducting qubits have made great strides in overcoming decoherence, improving the prospects for scalability and have become one of the leading contenders for the development of large-scale quantum circuits. In this Review, we describe the current state of the art in semiconductor charge and spin qubits based on gate-controlled semiconductor quantum dots, shallow dopants and colour centres in wide-bandgap materials. We frame the relative strengths of the different semiconductor qubit implementations in the context of applications such as quantum simulation, computing, sensing and networks. By highlighting the status and future perspectives of the basic types of semiconductor qubits, this Review aims to serve as a technical introduction for non-specialists and a forward-looking reference for scientists intending to work in this field. Semiconductor qubits are expected to have diverse future quantum applications. This Review discusses semiconductor qubit implementations from the perspective of an ecosystem of applications, such as quantum simulation, sensing, computation and communication.
180 citations
References
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Book•
01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Abstract: Part I Fundamental Concepts: 1 Introduction and overview 2 Introduction to quantum mechanics 3 Introduction to computer science Part II Quantum Computation: 4 Quantum circuits 5 The quantum Fourier transform and its application 6 Quantum search algorithms 7 Quantum computers: physical realization Part III Quantum Information: 8 Quantum noise and quantum operations 9 Distance measures for quantum information 10 Quantum error-correction 11 Entropy and information 12 Quantum information theory Appendices References Index
25,929 citations
TL;DR: Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.
Abstract: In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.
13,778 citations
TL;DR: In this article, it was shown that even without such a separability or locality requirement, no hidden variable interpretation of quantum mechanics is possible and that such an interpretation has a grossly nonlocal structure, which is characteristic of any such theory which reproduces exactly the quantum mechanical predictions.
Abstract: THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables These additional variables were to restore to the theory causality and locality [2] In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty There have been attempts [3] to show that even without such a separability or locality requirement no "hidden variable" interpretation of quantum mechanics is possible These attempts have been examined elsewhere [4] and found wanting Moreover, a hidden variable interpretation of elementary quantum theory [5] has been explicitly constructed That particular interpretation has indeed a grossly nonlocal structure This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions
10,253 citations
TL;DR: In this article, an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix was conjectured.
Abstract: The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state $\ensuremath{\rho}$ is the minimum average entanglement of an ensemble of pure states that represents \ensuremath{\rho}. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.
6,999 citations
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TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
Abstract: All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized
6,980 citations