Relevant bibliographies by topics / Heisenberg limit

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Heisenberg limit'

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Published: 25 May 2024

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Journal articles on the topic "Heisenberg limit"

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Gaete, Patricio. "Some Remarks on Nonlinear Electrodynamics." Advances in High Energy Physics 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/2463203.

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By using the gauge-invariant, but path-dependent, variables formalism, we study both massive Euler-Heisenberg-like and Euler-Heisenberg-like electrodynamics in the approximation of the strong-field limit. It is shown that massive Euler-Heisenberg-type electrodynamics displays the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of electrodynamics. As a result, for the case of massive Euler-Heisenbeg-like electrodynamics (Wichmann-Kroll), unexpected features are found. We obtain a new long-range (1/r3-type) correction, apart from a long-range(1/r5-type) correction to the Coulomb potential. Furthermore, Euler-Heisenberg-like electrodynamics in the approximation of the strong-field limit (to the leading logarithmic order) displays a long-range (1/r5-type) correction to the Coulomb potential. Besides, for their noncommutative versions, the interaction energy is ultraviolet finite.
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Putra, Fima Ardianto. "De Broglie Wave Analysis of the Heisenberg Uncertainty Minimum Limit under the Lorentz Transformation." Jurnal Teras Fisika 1, no. 2 (September 20, 2018): 1. http://dx.doi.org/10.20884/1.jtf.2018.1.2.1008.

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A simple analysis using differential calculus has been done to consider the minimum limit of the Heisenberg uncertainty principle in the relativistic domain. An analysis is made by expressing the form of and based on the Lorentz transformation, and their corresponding relation according to the de Broglie wave packet modification. The result shows that in the relativistic domain, the minimum limit of the Heisenberg uncertainty is p x ?/2 and/or E t ?/2, with is the Lorentz factor which depend on the average/group velocity of relativistic de Broglie wave packet. While, the minimum limit according to p x ?/2 or E t ?/2, is the special case, which is consistent with Galilean transformation. The existence of the correction factor signifies the difference in the minimum limit of the Heisenberg uncertainty between relativistic and non-relativistic quantum. It is also shown in this work that the Heisenberg uncertainty principle is not invariant under the Lorentz transformation. The form p x ?/2 and/or E t ?/2 are properly obeyed by the Klein-Gordon and the Dirac solution. Key words: De Broglie wave packet, Heisenberg uncertainty, Lorentz transformation, and minimum limit.
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Luis, Alfredo. "Nonlinear transformations and the Heisenberg limit." Physics Letters A 329, no. 1-2 (August 2004): 8–13. http://dx.doi.org/10.1016/j.physleta.2004.06.080.

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SIOPSIS, GEORGE. "THE PENROSE LIMIT OF AdS×S SPACE AND HOLOGRAPHY." Modern Physics Letters A 19, no. 12 (April 20, 2004): 887–95. http://dx.doi.org/10.1142/s0217732304013891.

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In the Penrose limit, AdS ×S space turns into a Cahen–Wallach (CW) space whose Killing vectors satisfy a Heisenberg algebra. This algebra is mapped onto the holographic screen on the boundary of AdS. We show that the Heisenberg algebra on the boundary of AdS may be obtained directly from the CW space by appropriately constraining the states defined on it. The transformations generated by the constraint are similar to gauge transformations. The "holographic screen" on the CW space is thus obtained as a "gauge-fixing" condition.
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Sanchidrián-Vaca, Carlos, and Carlos Sabín. "Parameter Estimation of Wormholes beyond the Heisenberg Limit." Universe 4, no. 11 (November 6, 2018): 115. http://dx.doi.org/10.3390/universe4110115.

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We propose to exploit the quantum properties of nonlinear media to estimate the parameters of massless wormholes. The spacetime curvature produces a change in length with respect to Minkowski spacetime that can be estimated in principle with an interferometer. We use quantum metrology techniques to show that the sensitivity is improved with nonlinear media and propose a nonlinear Mach–Zehnder interferometer to estimate the parameters of massless wormholes that scales beyond the Heisenberg limit.
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Napolitano, M., M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell, and M. W. Mitchell. "Quantum Optics and the “Heisenberg Limit” of Measurement." Optics and Photonics News 22, no. 12 (December 1, 2011): 40. http://dx.doi.org/10.1364/opn.22.12.000040.

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Ohring, Peter. "A central limit theorem on Heisenberg type groups." Proceedings of the American Mathematical Society 113, no. 2 (February 1, 1991): 529. http://dx.doi.org/10.1090/s0002-9939-1991-1045146-7.

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Maleki, Yusef, and Aleksei M. Zheltikov. "Spin cat-state family for Heisenberg-limit metrology." Journal of the Optical Society of America B 37, no. 4 (March 10, 2020): 1021. http://dx.doi.org/10.1364/josab.374221.

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Unternährer, Manuel, Bänz Bessire, Leonardo Gasparini, Matteo Perenzoni, and André Stefanov. "Super-resolution quantum imaging at the Heisenberg limit." Optica 5, no. 9 (September 20, 2018): 1150. http://dx.doi.org/10.1364/optica.5.001150.

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TSVELIK, A. M. "TWO WEAKLY COUPLED HEISENBERG CHAINS—SOLUTION IN CONTINUOUS LIMIT." Modern Physics Letters B 05, no. 30 (December 30, 1991): 1973–79. http://dx.doi.org/10.1142/s0217984991002379.

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Using the bosonization procedure proposed for the spin-1/2 Heisenberg chain in Ref. 8 we obtain the effective Hamiltonian for the system of two weakly coupled Heisenberg chains with the XXZ anisotropy as the sum of two sine-Gordon Hamiltonians. It appears that this simple system reveals a rather rich variety of properties in different regions of anisotropy. We calculate the spin-spin correlation functions; two-spin correlation functions decay exponentially but there are regions where the four-spin correlation functions decay as a power law. In particular, if both the inter- and intrachain exchange interactions are isotropic and the interchain exchange is ferromagnetic correlations of the chirality field χ= S 1× S 2 (the indexes 1 and 2 numerate the chains) are enhanced and their correlation functions follow a power law. In this case coupling between pairs of chains can lead to chiral ordering in three dimensions.
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Dissertations / Theses on the topic "Heisenberg limit"

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Exler, Matthias. "On classical and quantum mechanical energy spectra of finite Heisenberg spin systems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980110440.

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Shettell, Nathan. "Quantum Information Techniques for Quantum Metrology." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS504.

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La métrologie quantique est une discipline prometteuse de l'information quantique qui connaît actuellement une vague de percées expérimentales et de développements théoriques. L'objectif principal de la métrologie quantique est d'estimer des paramètres inconnus aussi précisément que possible. En utilisant des ressources quantiques comme sondes, il est possible d'atteindre une précision de mesure qui serait autrement impossible en utilisant les meilleures stratégies classiques. Par exemple, en ce qui concerne la tâche d'estimation de la phase, la précision maximale (la limite d'Heisenberg) est un gain de précision quadratique par rapport aux meilleures stratégies classiques. Bien entendu, la métrologie quantique n'est pas la seule technologie quantique qui connaît actuellement des avancées. Le thème de cette thèse est l'exploration de la manière dont la métrologie quantique peut être améliorée par d'autres techniques quantiques lorsque cela est approprié, à savoir : les états graphiques, la correction d'erreurs et la cryptographie. Les états de graphes sont une ressource incroyablement utile et polyvalente dans l'information quantique. Nous aidons à déterminer l'étendue de l'applicabilité des états de graphes en quantifiant leur utilité pour la tâche de métrologie quantique de l'estimation de phase. En particulier, l'utilité d'un état de graphe peut être caractérisée en fonction de la forme du graphe correspondant. À partir de là, nous concevons une méthode pour transformer tout état de graphe en un état de graphe plus grand (appelé "bundled graph states") qui sature approximativement la limite de Heisenberg. En outre, nous montrons que les états de graphe constituent une ressource robuste contre les effets du bruit (le déphasage et un petit nombre d'effacements) et que la limite quantique de Cramér-Rao peut être saturée par une simple stratégie de mesure. Le bruit issu de l’environnement est l'un des principaux obstacles à la métrologie quantique, qui limite la précision et la sensibilité qu'elle peut atteindre. Il a été démontré que si le bruit environnemental peut être distingué de la dynamique de la tâche de métrologie quantique, des applications fréquentes de correction d'erreurs peuvent être utilisées pour combattre les effets du bruit. En pratique, cependant, la fréquence de correction d'erreurs requise pour maintenir une précision de type Heisenberg est impossible à atteindre pour les technologies quantiques actuelles. Nous explorons les limites de la métrologie quantique améliorée par la correction d'erreurs en prenant en compte les contraintes et les obstacles technologiques, à partir desquels nous établissons le régime dans lequel la limite d'Heisenberg peut être maintenue en présence de bruit. La mise en œuvre complète d'un problème de métrologie quantique est technologiquement exigeante : des états quantiques intriqués doivent être générés et mesurés avec une grande fidélité. Une solution, dans le cas où l'on ne dispose pas de tout le matériel quantique nécessaire, consiste à déléguer une tâche à un tiers. Ce faisant, plusieurs problèmes de sécurité se posent naturellement en raison de la possibilité d'interférence d'un adversaire malveillant. Nous abordons ces questions en développant la notion de cadre cryptographique pour la métrologie quantique. Nous montrons que la précision du problème de la métrologie quantique peut être directement liée à la solidité d'un protocole cryptographique employé. En outre, nous développons des protocoles cryptographiques pour une variété de paramètres motivés par la cryptographie, à savoir : la métrologie quantique sur un canal quantique non sécurisé et la métrologie quantique avec une tâche déléguée à une partie non fiable. Les réseaux de détection quantique ont suscité un intérêt croissant dans la communauté de la métrologie quantique au cours des dernières années. Ils constituent un choix naturel pour les problèmes distribués dans l'espace et les problèmes multiparamètres.[...]
Quantum metrology is an auspicious discipline of quantum information which is currently witnessing a surge of experimental breakthroughs and theoretical developments. The main goal of quantum metrology is to estimate unknown parameters as accurately as possible. By using quantum resources as probes, it is possible to attain a measurement precision that would be otherwise impossible using the best classical strategies. For example, with respect to the task of phase estimation, the maximum precision (the Heisenberg limit) is a quadratic gain in precision with respect to the best classical strategies. Of course, quantum metrology is not the sole quantum technology currently undergoing advances. The theme of this thesis is exploring how quantum metrology can be enhanced with other quantum techniques when appropriate, namely: graph states, error correction and cryptography. Graph states are an incredibly useful and versatile resource in quantum information. We aid in determining the full extent of the applicability of graph states by quantifying their practicality for the quantum metrology task of phase estimation. In particular, the utility of a graph state can be characterised in terms of the shape of the corresponding graph. From this, we devise a method to transform any graph state into a larger graph state (named a bundled graph state) which approximately saturates the Heisenberg limit. Additionally, we show that graph states are a robust resource against the effects of noise, namely dephasing and a small number of erasures, and that the quantum Cramér-Rao bound can be saturated with a simple measurement strategy. Noise is one of the biggest obstacles for quantum metrology that limits its achievable precision and sensitivity. It has been showed that if the environmental noise is distinguishable from the dynamics of the quantum metrology task, then frequent applications of error correction can be used to combat the effects of noise. In practise however, the required frequency of error correction to maintain Heisenberg-like precision is unobtainable for current quantum technologies. We explore the limitations of error correction enhanced quantum metrology by taking into consideration technological constraints and impediments, from which, we establish the regime in which the Heisenberg limit can be maintained in the presence of noise. Fully implementing a quantum metrology problem is technologically demanding: entangled quantum states must be generated and measured with high fidelity. One solution, in the instance where one lacks all of the necessary quantum hardware, is to delegate a task to a third party. In doing so, several security issues naturally arise because of the possibility of interference of a malicious adversary. We address these issues by developing the notion of a cryptographic framework for quantum metrology. We show that the precision of the quantum metrology problem can be directly related to the soundness of an employed cryptographic protocol. Additionally, we develop cryptographic protocols for a variety of cryptographically motivated settings, namely: quantum metrology over an unsecured quantum channel and quantum metrology with a task delegated to an untrusted party. Quantum sensing networks have been gaining interest in the quantum metrology community over the past few years. They are a natural choice for spatially distributed problems and multiparameter problems. The three proposed techniques, graph states, error correction and cryptography, are a natural fit to be immersed in quantum sensing network. Graph states are an well-known candidate for the description of a quantum network, error correction can be used to mitigate the effects of a noisy quantum channel, and the cryptographic framework of quantum metrology can be used to add a sense of security. Combining these works formally is a future perspective
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Tashiro, Kenshiro. "Gromov-Hausdorff limits of compact Heisenberg manifolds with sub-Riemannian metrics." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263433.

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Baker, Travis J. "Quantum correlations: Schrodinger's steering in lossy conditions; Heisenberg's limit to laser coherence." Thesis, Griffith University, 2021. http://hdl.handle.net/10072/405636.

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Quantum correlations are a fundamental resource for technologies arising out of quantum information science. This thesis contains a body of work consisting of published and unpublished papers, which document theoretical developments in two active topics within this field - Einstein-Podolsky-Rosen (EPR) steering, and optical laser coherence. While these two topics might seem unrelated at first glance, all results contained within this work fundamentally arise from exploring the correlations between nonlocal quantum systems of low dimension. As such, this thesis is composed of two parts. The first is dedicated to studies of EPR steering, where one observer can appear to remotely steer (in the terminology of Schrodinger) the state of a distant party into different ensembles of quantum states. A number of novel results are presented which address the fundamental problem of determining both steerability and non-steerability of bipartite quantum states. Motivated by experiments aiming to demonstrate one-way steering, we begin by deriving a condition that can be applied to any two-qubit state, which is sufficient to determine if it is non-steerable when passed through a channel with a given amount of loss. This result is further expanded in the context of a new experiment, and applied to tomographically reconstructed two-qubit states which demonstrate one-way EPR steering in this rigorous way for the first time. Next, we develop a different idea for proving non-steerability of two-qubit entangled states, based on the idea of allowing the steering party to perform deterministic local quantum operations prior to measuring. Finally, we turn to the general issue of certifying steerability while closing the detection loophole, which has been previously closed in a number of experiments by violating specific loss-tolerant steering inequalities. Introducing a semi-definite programming formulation of the problem, we exploit the symmetry of a class of quantum states which naturally arise in quantum networks (the so-called inept states), to efficiently calculate the amount of loss they can tolerate while maintaining steerability. The collection of results in this first part are expected to be useful, especially as the field moves toward applications in networks where qubit loss becomes a limiting factor. The second part of this thesis concerns a defining property of a laser beam-optical coherence. This can be quantified by a dimensionless number, C, which can be roughly understood as the mean number of photons emitted into the beam with the same phase. While the fundamental theory of practical laser systems was developed in the 1950's and 60's, the ultimate quantum limits to the coherence of the beams a laser can produce has not been previously studied. In terms of the mean number of excitations stored inside the laser cavity, μ, it was previously thought that C = ø(μ2). Here, under some natural assumptions we show analytically that the ultimate limit permitted by quantum theory, or the Heisenberg limit, is quadratically better; C = O(μ4). Moreover, by treating the beam produced by a laser cavity as an infinite chain of entangled qubits, we use state-of-the-art matrix product state methods to numerically find a model of laser dynamics which attains this new ultimate limit. That is, C = ø(μ4). Finally, we present a system constructed with technology already existing in the field of circuit quantum electrodynamics, and use techniques from quantum control to prove that a coherent train of pulses attaining this limit can be created. The results presented in this part are a prescription for engineering a laser system operating at the best possible limit.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Environment and Sc
Science, Environment, Engineering and Technology
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Benoit, Jérôme. "Symétrie, géométrie, topologie et spins : spins de Heisenberg à la limite continue, membranes magnétiques." Cergy-Pontoise, 1999. http://www.theses.fr/1999CERG0076.

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Kipper, Carla Judite. "Emprego da parametrização de heisenberg e do método de adomian no decaimento da camada limite convectiva." Universidade Federal de Santa Maria, 2009. http://repositorio.ufsm.br/handle/1/3893.

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In this paper we present a spectral model to describe the decay of turbulent kinetic energy in the Convective Boundary Layer (CLC) of the earth s surface, where the physical processes that occur generate turbulence of convective origin and mechanics in the air. Using the equations of conservation of time, which describe the dynamics of an element of fluid in a flow, you get an equation for the spectrum of kinetic energy in a homogeneous turbulent flow, but not isotropic. The spectrum of energy is expressed in terms of number of wave vector kappa and time. Each term in this equation of energy balance, describing different physical processes that generate the turbulence. The terms of production or loss of energy by the effect of heat and friction, are written according to the number of Richardson, which is a dimensionless quantity that expresses a relationship between potential energy and kinetic energy of a fluid. The term transfer of kinetic energy by inertial effect between eddies of different wave numbers is parameterized from the Heisenberg model which, based on intuitive arguments, assume that the transfer of energy between eddies with small number of wave for the large number of wavelength is similar to conversion of mechanical energy into heat energy, the effect of molecular viscosity. The number of eddies with wave absorbing higher energy of eddies of wave number with lower. The dynamic equation for the three-dimensional spectrum of kinetic energy obtained was solved by the Adomian decomposition method for the analytical solution of ordinary differential equations or partial, linear or nonlinear, deterministic or stochastic. This technique is to decompose a given equation into a linear part and one non-linear, isolating the operator linear, easily inverted of higher order. The nonlinear term is written as a sum of a special class of polynomials called Adomian polynomials of, and unknown function as a series whose terms are calculated on recursively. The application of the Adomian decomposition method for the solution of differential equation integrated non linear due to the spectrum of kinetic energy, has an analytical solution without linearization, commonly used for simplicity, in problems where processes are highly nonlinear. Moreover, due to rapid convergence of the solution in terms of the Adomian polynomials, the spectrum of kinetic energy was obtained without a large computational effort. From the calculation of the energy spectrum could be determined the variation of turbulent kinetic energy in the CLC and compared with results of numerical simulation in the literature.
No presente trabalho é apresentado um modelo espectral para descrever o decaimento da energia cinética turbulenta na Camada Limite Convectiva (CLC) da superfície terrestre, onde acontecem os processos físicos que geram turbulência de origem mecânica e convectiva no ar. Partindo das equações de conservação de momento, que descrevem a dinâmica de um elemento de fluído em um escoamento, se obtém uma equação para o espectro de energia cinética em um escoamento turbulento homogêneo, mas não isotrópico. O espectro de energia é expresso em termos do vetor número de onda κ e do tempo. Cada termo, nesta equaçaão de balanço de energia, descreve processos físicos distintos que geram a turbulência. Os termos de produção ou perda de energia por efeito térmico e por atrito, são escritos em função do número de Richardson, que é uma grandeza adimensional que expressa uma relação entre a energia potencial e a energia cinética de um fluído. O termo de transferência de energia cinética por efeito inercial entre os turbilhões de diferentes números de onda é parametrizado a partir do modelo de Heisenberg que, baseando-se em argumentos intuitivos, assume que o processo de transferência de energia entre turbilhões com pequeno número de onda para os de número de onda grande, é similar a conversão de energia mecânica em energia térmica, por efeito de uma viscosidade molecular. Os turbilhões com número de onda maior absorvem energia dos turbilhões com número de onda menor. A equação dinâmica para o espectro de energia cinética tridimensional obtida foi resolvida pelo método da decomposição de Adomian para solução analítica de equações diferenciais ordinárias ou parciais, lineares ou não lineares, determinísticas ou estocásticas. Esta técnica consiste em decompor uma dada equação em uma parte linear e outra não-linear, isolando o operador linear, facilmente inversível, de maior ordem. O termo não-linear é escrito como uma soma de uma classe especial de polinômios, denominados Polinômios de Adomian, e a função desconhecida como uma série, cujos termos são calculados de forma recursiva. A aplicação do método de decomposição de Adomian na solução da equação integro-diferencial não linear resultante para o espectro de energia cinética, permitiu uma solução analítica sem a linearização, comumente usada por simplicidade, em problemas onde se têm processos altamente não lineares. Além disso, devido a rápida convergência da solução expressa em termos dos polinômios de Adomian, o espectro de energia cinética foi obtido sem uma grande esforço computacional. A partir do cálculo do espectro de energia pôde-se determinar a variação da energia cinética turbulenta na CLC e comparar com os resultados de simulação numérica existentes na literatura.
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Conti, William Remo Pedroso. "Teorema Central do Limite para o modelo O(N) de Heisenberg hierárquico na criticalidade e o papel do limite N -> infinito na dinâmica dos zeros de Lee-Yang." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-26082008-093457/.

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Neste trabalho estabelecemos o Teorema Central do Limite para o modelo O(N) de Heisenberg hierárquico na criticalidade via equação a derivadas parciais no limite N -> infinito. Por simplicidade consideramos apenas o caso d = 4, sendo o teorema também válido para d > 4. Pelo estudo de uma dada equação a derivadas parciais (EDP) determinamos a temperatura inversa crítica do modelo esférico hierárquico contínuo para um d > 2 qualquer, havendo conexão entre criticalidade e o ponto fixo da EDP. Por meio de uma análise geométrica da trajetória crítica obtemos informações sobre a dinâmica e distribuição dos zeros de Lee-Yang.
In this work we stablish the Central Limit Theorem for the hierarchical O(N) Heisenberg model at criticality via partial differential equation in the limit N -> infinity. For simplicity we only treat the d = 4 case but the theorem is still valid for d > 4. By studying a given partial differential equation (PDE) we determine for any d > 2 the critical inverse temperature of the continuum hierarchical spherical model, and we show a connection between criticality and the fixed point of PDE. By means of a geometric analysis of the critical trajectory we obtain some informations about Lee-Yang zeros´s dynamics and distribution.
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Facon, Adrien. "Chats de Schrödinger d'un atome de Rydberg pour la métrologie quantique." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066534/document.

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Il n'y a pas de limite fondamentale à une mesure classique : la position d'une aiguille sur un cadran peut être déterminée avec une incertitude arbitrairement faible. Au contraire, dans le monde quantique, la précision de toute mesure est limitée par le bruit quantique. Lorsque l'aiguille de mesure devient un système mésoscopique, tel un moment cinétique J qui évoluerait sur le cadran sphérique d'une sphère de Bloch, les fluctuations quantiques affectant les états cohérents conduisent alors à une incertitude de mesure en 1/√J appelée limite quantique standard. La métrologie quantique consiste à préparer l'aiguille dans un état quantique qui permet de dépasser cette limite et d'atteindre la précision ultime fondamentale, dite limite de Heisenberg, qui évolue en 1/J. Nous proposons et réalisons une approche innovante fondée sur la mesure de la phase relative d'une superposition d'états mésoscopiques du type Chat de Schrödinger. En utilisant un champ radiofréquence polarisé, nous avons en effet pu préparer un atome de Rydberg dans une superposition quantique du moment cinétique décrivant l'électron, dont la sensibilité au champ électrique approche la limite de Heisenberg. Cette méthode a permis la réalisation d'un électromètre à un seul atome mesurant de faibles champs de l'ordre du mV/cm en quelques dizaines de nanosecondes. La grande sensibilité de ces méthodes de mesure de champ résolue en temps et en espace ouvre la voie à de nombreuses applications
There is no fundamental limit to the precision of a classical measurement. The position of a meter’s needle can be determined with an arbitrarily small uncertainty. In the quantum realm, fundamental fluctuations due to the Heisenberg principle limit the precision of any measurement. When the needle is replaced by a mesoscopic system, for instance a spin J evolving on a spherical dial, the Bloch sphere, the semi-classical spin coherent state quantum fluctuations lead to a measurement uncertainty scaling as 1/√J, the standard quantum limit (SQL). This is far from the ultimate Heisenberg limit (HL), which scales as 1/J. We present here an innovative approach, using interferometric measurements on mesoscopic Schrödinger-cat-like superpositions of Rydberg states to realize a single-atom electrometer measuring weak fields of the order of 1 mV/cm in a few tens of nanoseconds. The sensitivity of this method is beyond the SQL and we check that its uncertainty scales as the HL. The extreme sensitivity of this non-invasive space- and time-resolved field measurement could have many practical applications
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Books on the topic "Heisenberg limit"

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Neuenschwander, Daniel. Probabilities on the Heisenberg group: Limit theorems and Brownian motion. Berlin: Springer, 1996.

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Probabilities on the Heisenberg group: Limit theorems and Brownian motion. Berlin: Springer, 1996.

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Neuenschwander, Daniel. Probabilities on the Heisenberg Group: Limit Theorems and Brownian Motion. Springer London, Limited, 2006.

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Book chapters on the topic "Heisenberg limit"

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LaPierre, Ray. "Heisenberg Limit." In Getting Started in Quantum Optics, 165–75. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-12432-7_17.

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Neuenschwander, Daniel. "Other limit theorems on H." In Probabilities on the Heisenberg Group, 85–123. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0094033.

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Croca, Josee R. "Beyond Heisenberg’S Uncertainty Limits." In Gravitation and Cosmology: From the Hubble Radius to the Planck Scale, 385–92. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-48052-2_38.

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Schmidt-Böcking, H., S. Eckart, H. J. Lüdde, G. Gruber, and T. Jahnke. "The Precision Limits in a Single-Event Quantum Measurement of Electron Momentum and Position." In Molecular Beams in Physics and Chemistry, 223–45. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63963-1_12.

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AbstractA modern state-of-the-art “quantum measurement” [The term “quantum measurement” as used here implies that parameters of atomic particles are measured that emerge from a single scattering process of quantum particles.] of momentum and position of a single electron at a given time [“at a given time” means directly after the scattering process. (It should be noticed that the duration of the reaction process is typically extremely short => attoseconds).] and the precision limits for their experimental determination are discussed from an experimentalists point of view. We show—by giving examples of actually performed experiments—that in a single reaction between quantum particles at a given time only the momenta of the emitted particles but not their positions can be measured with sub-atomic resolution. This fundamental disparity between the conjugate variables of momentum and position is due to the fact that during a single-event measurement only the total momentum but not position is conserved as function of time. We highlight, that (other than prevalently perceived) Heisenberg’s “Uncertainty Relation” UR [1] does not limit the achievable resolution of momentum in a single-event measurement. Thus, Heisenberg’s statement that in a single-event measurement only either the position or the momentum (velocity) of a quantum particle can be measured with high precision contradicts a real experiment. The UR states only a correlation between the mean statistical fluctuations of a large number of repeated single-event measurements of two conjugate variables. A detailed discussion of the real measurement process and its precision with respect to momentum and position is presented.
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Eckle, Hans-Peter. "Finite Heisenberg Quantum Spin Chain." In Models of Quantum Matter, 667–86. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0020.

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The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of finite-size scaling and conformal symmetry in finite geometries. The mathematical techniques introduced in chapter 19 permit a systematic treatment in this chapter of finite-size corrections as corrections to the thermodynamic limit of the system. The application of the Euler-Maclaurin formula transforming finite sums into integrals and finite-size corrections transforms the Bethe ansatz equations into Wiener–Hopf integral equations with inhomogeneities representing the finite-size corrections solvable using the Wiener–Hopf technique. The results can be compared to results for finite systems obtained from other approaches that are independent of the Bethe ansatz method. It briefly discusses higher-order corrections and offers a general assessment of the finite-size method.
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Eckle, Hans-Peter. "Bethe Ansatz for the Anisotropic Heisenberg Quantum Spin Chain." In Models of Quantum Matter, 502–44. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199678839.003.0014.

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This chapter verifies the conjecture for the wave function, the Bethe ansatz wave function, of the anisotropic Heisenberg quantum spin chain by examining first the cases for one, two, and three spin deviations. The equations determining the quasi- momenta are the Bethe ansatz equations, now obtained from the coordinate Bethe ansatz. The Bethe ansatz equations derive from the eigenvalue equation in combination with boundary conditions, here periodic boundary conditions. These quasi-momenta also determine the energy eigenvalue. However, solving the Bethe ansatz equations to obtain a particular state requires more considerations. New variables, called rapidities, are useful. The consideration of the thermodynamic limit then allows to extract information about the ground state and low-lying excitations of the anisotropic quantum spin chain from the Bethe ansatz equations. Furthermore, complex solutions of the Bethe ansatz equations, called strings, are considered.
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Bertlmann, Reinhold A., and Nicolai Friis. "Quantum Metrology." In Modern Quantum Theory, 777–816. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780199683338.003.0024.

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Abstract Chapter 24 provides a compact introduction to the topic of quantum metrology, focusing on Hamiltonian parameter estimation in the frequentist and in the Bayesian paradigms. We first discuss how estimates of non-directly measurable quantities such as phases are obtained from measurement statistics in the frequentist approach. We then discuss the Cramér-Rao bound and the Fisher information and study single-qubit phase estimation in the light of this result. We then turn to the multi-qubit setting and discuss the quantum Cramér-Rao bound, for which the quantum Fisher information is the central quantity of interest. In this context we discuss the Uhlmann fidelity in detail. We further contrast Heisenberg scaling with the standard quantum limit in the phase-estimation scenario. Finally, we analyse phase estimation in the Bayesian-estimation approach and derive the van Trees inequality as a Bayesian version of the Cramér-Rao bound
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Clerk, Aashish A. "Optomechanics and Quantum Measurement." In Quantum Optomechanics and Nanomechanics, 183–236. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198828143.003.0005.

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After a quick review of the basic theory of quantum optomechanical systems, based largely on linearized Heisenberg–Langevin equations, this chapter focuses on selected topics related to quantum measurement and quantum optomechanics. Included are: a comprehensive discussion of the quantum limit on the added noise of a continuous position detector, following the quantum linear response approach; a detailed discussion of the role of noise correlations, and how these can be achieved in an optomechanical cavity (by using squeezed input light, or by modifying the choice of measured output quadrature); and a discussion of back-action evading measurements of a mechanical quadrature, discussing how this can be achieved in a two-tone driven cavity system. The chapter ends with a quick introduction to the theory of conditional continuous quantum measurement, and a discussion on how a back-action evading measurement can be used to produce conditional mechanical squeezed states.
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Gherdjikov, Serghey Stoilov. "The Limits of Science." In The Paideia Archive: Twentieth World Congress of Philosophy, 80–87. Philosophy Documentation Center, 1998. http://dx.doi.org/10.5840/wcp20-paideia199837655.

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Does science have any limits? Scientists say no. Philosophers are divided in their response. The humanities say that science is not "humanitarian," and thus not metaphysically deep. In response, scientists and some philosophers contend that science is the best knowledge we have about the world. I argue that science is limited by its form. Science has no object that derives from the human form. Everything that is incomparable to the dimension of the human body is reducible to notions that are commensurable to that body. This phenomenologically clarifies some of the most important discoveries in contemporary science. The Special Theory of Relativity shows the dependence of space and time on the accounting system. Quantum mechanics displays the limits of observation (Heisenberg) and logical indefiniteness by compelling the creation of a macropresentation of micro-objects and gets around logic (Feyerabend) through the principle of additionality. Experimental science has come out as an artificial projection of human expansion, not as a reflection of the transcendent order of the world itself. "The life world" successfully takes the place of "the objective world" of modern rationality.
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"Chap. 5: About the limits of the knowledge of nature." In My Life with Science (extendes English edition), 95–102. GNT-Verlag GmbH, 2023. http://dx.doi.org/10.47261/1558-5.

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“... Although I am a physicist by training, I am predominantly associated with chemistry. I would like to quote two prominent representatives of my field on the relationship between the two disciplines: “A chemist who is not a physicist is nothing at all” (Robert Wilhelm Bunsen) and “The really interesting thing about physics is chemistry” (Fritz Haber). When the young Max Planck expressed the wish to study physics, he was advised against it because it was considered a closed science at the time. But then he himself took a decisive step to overturn this view. Then came Albert Einstein and Werner Heisenberg and revolutionized the physical worldview.” ...
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Conference papers on the topic "Heisenberg limit"

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Wiseman, Howard M., S. Nariman Saadatmand, Travis J. Baker, and Dominic W. Berry. "The Heisenberg limit for laser coherence." In Conference on Coherence and Quantum Optics. Washington, D.C.: OSA, 2019. http://dx.doi.org/10.1364/cqo.2019.m3a.1.

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Walter, Michael, and Joseph M. Renes. "A Heisenberg limit for quantum region estimation." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875008.

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Tsarev, D. V., Ngo-The Vinh, and A. P. Alodjants. "Beating Heisenberg limit with moving matter-wave solitons." In 2020 International Conference Laser Optics (ICLO). IEEE, 2020. http://dx.doi.org/10.1109/iclo48556.2020.9285804.

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Jin, Xian-Min, Martin Lebrat, Lijian Zhang, Kachung Lee, Tim Bartley, Marco Barbieri, Joshua Nunn, Animesh Datta, and Ian A. Walmsley. "Surpassing the conventional Heisenberg limit using classical resources." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2013. http://dx.doi.org/10.1364/cleo_qels.2013.qf2b.2.

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Unternährer, Manuel, Bänz Bessire, Leonardo Gasparini, Matteo Perenzoni, and André Stefanov. "Super-Resolution Quantum Imaging at the Heisenberg Limit." In CLEO: QELS_Fundamental Science. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/cleo_qels.2018.ff1b.4.

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Tsarev, D. V., Ray-Kuang Lee, and A. P. Alodjants. "Quantum metrology beyond Heisenberg limit with entangled matter wave solitons." In 2018 International Conference Laser Optics (ICLO). IEEE, 2018. http://dx.doi.org/10.1109/lo.2018.8435438.

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Kolkiran, Aziz, and G. S. Agarwal. "Towards Heisenberg Limit in Magnetometry with Parametric Down Converted Photons." In Laser Science. Washington, D.C.: OSA, 2006. http://dx.doi.org/10.1364/ls.2006.ltha5.

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Bessire, Bänz, Manuel Unternährer, Leonardo Gasparini, Majid Zarghami, Matteo Perenzoni, and André Stefanov. "Super-resolution quantum imaging at the Heisenberg limit (Conference Presentation)." In Quantum Technologies, edited by Andrew J. Shields, Jürgen Stuhler, and Miles J. Padgett. SPIE, 2018. http://dx.doi.org/10.1117/12.2309773.

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Napolitano, Mario, Marco Koschorreck, Brice Dubost, Naeimeh Behbood, Robert Sewell, and Morgan W. Mitchell. "Interaction-based Quantum Metrology Showing Scaling Beyond the Heisenberg Limit." In Quantum Information and Measurement. Washington, D.C.: OSA, 2012. http://dx.doi.org/10.1364/qim.2012.qw1b.2.

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Ostrowski, Lucas A., Travis J. Baker, S. Nariman Saadatmand, and Howard M. Wiseman. "No Tradeoff between Coherence and Sub-Poissonianity in Heisenberg-Limited Lasers." In Frontiers in Optics. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/fio.2022.jw4a.86.

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Let ℭ be the number of photons in a coherence time of a laser beam. The Heisenberg limit is ℭ = O(µ4), lying beyond the standard limit of ℭ = O(µ2). Here, we generalise this result for sub-Poissonian beams.
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