Quantum limits in image processing

We analyze the information content of density profiles for an ultracold Bose gas of atoms and extract resolution limits for observables contained in these images. Our starting point is density correlations that we compute within the Bogoliubov approximation, taking into account quantum and thermal fluctuations beyond mean-field theory. This provides an approximate way to construct the joint counting statistics of atoms in an array of pixels covering the gas. We derive the Fisher information of an image and the associated Cramér-Rao sensitivity bound for measuring observables contained in the image. We elaborate on our recent study on position measurements of a dark soliton [Negretti et al., Phys. Rev. A 77, 043606 (2008)] where a sensitivity scaling with the atomic density as n −3/4 was found. We discuss here a wider class of soliton solutions and present a detailed analysis of the Bogoliubov excitations and the gapless (Goldstone) excitation modes. These fluctuations around the mean field contribute to the noise in the image, and we show how they can actually improve the ability to locate the position of the soliton.

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“…Given the image data ρ(x; q), we construct, as in Refs. [28,29], a linear filter g(x) to provide an estimate for q:…”

Section: Poissonian Counting Statisticsmentioning

confidence: 99%

“…This optimization problem has the following solution, as pointed out in Ref. [29] for a coherent state of light populating a single spatial mode:…”

Section: Poissonian Counting Statisticsmentioning

confidence: 99%

Quantum fluctuations in the image of a Bose gas

2008

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“…This has been first experimentally demonstrated for measurements in which the information about the parameter θ is carried by the total intensity [3] or by the phase [4] of a light beam. Later situations were considered where the parameter θ does not change the total intensity of the light but modifies the details of the repartition of light in the transverse plane [5] (for example to estimate a very small lateral displacement of a beam [6]). As the energy of the squeezed state increases with the squeezing factor, the ultimate limit with squeezed state for a fixed total energy scales as 1/N 3/4 .…”

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confidence: 99%

Ultimate sensitivity of precision measurements with intense Gaussian quantum light: A multimodal approach

et al. 2012

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Multimode Gaussian quantum light, which includes multimode squeezed and multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications in quantum information processing and metrology. In this paper, we determine the ultimate sensitivity in the estimation of any parameter when the information about this parameter is encoded in such light, irrespective of the information extraction protocol used in the estimation and of the measured observable. In addition we show that an appropriate homodyne detection scheme allows us to reach this ultimate sensitivity. We show that, for a given set of available quantum resources, the most economical way to maximize the sensitivity is to put the most squeezed state available in a well-defined light mode. This implies that it is not possible to take advantage of the existence of squeezed fluctuations in other modes, nor of quantum correlations and entanglement between different modes.

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“…The second example assumes that the mean intensity is large enough so as to invoke the Central Limit Theorem [19], but it considers the improvement that can be achieved when using nonclassical, squeezed light (see, e.g., [30][31][32]). Under these circumstances, squeezed light produces Gaussian noise statistics with variance s 2 n 0 , where s 2 < 1 is the squeezing factor [33,34]. The number of absorbed photons on a single detector is thus parameterized by the PDFs:…”

Section: A Noise Models and Fisher Informationmentioning

confidence: 99%

Information and resolution in electromagnetic optical systems

Foreman

Török

2010

Phys. Rev. A

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Quantitative analysis can play a vital role in a number of polarization-based optical systems, yet to date no definition regarding resolution in the polarization domain exists. By adopting a stochastic framework, a suitable metric is developed in this article, allowing a number of polarimetric systems to be assessed and compared. In so doing, the performance dependencies of polarization-based systems are demonstrated and fundamental trends are identified.

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Quantum limits in image processing

Cited by 60 publications

References 24 publications

Quantum fluctuations in the image of a Bose gas

Quantum fluctuations in the image of a Bose gas

Ultimate sensitivity of precision measurements with intense Gaussian quantum light: A multimodal approach

Information and resolution in electromagnetic optical systems

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