Quantum noise in multipixel image processing

Treps, Nicolas; Delaubert, V.; Maître, Agnès; Courty, Jean-Michel; Fabre, Claude

doi:10.1103/physreva.71.013820

Cited by 81 publications

(68 citation statements)

References 16 publications

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“…Spatial squeezing has been defined for any linear measurement performed with an array detector [26]. Similarly, spatial entanglement corresponding to any linear measurement, can be obtained.…”

Section: Entanglement Schemementioning

confidence: 99%

Continuous-variable spatial entanglement for bright optical beams

et al. 2005

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A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.

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Section: Entanglement Schemementioning

confidence: 99%

Continuous-variable spatial entanglement for bright optical beams

et al. 2005

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“…(8) can then be performed analytically. When we take the limit of infinitely small pixels, one finds an integral over the spatial coordinate of the image [28] …”

Section: Poissonian Counting Statisticsmentioning

confidence: 99%

“…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%

Quantum fluctuations in the image of a Bose gas

2008

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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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“…3 of the main text and correspond to a compromise between signal to noise ratio and visibility amplitude. As we shrink the integration volumes, the dip visibility first increases and then reaches a saturation value, meaning that the integration volume becomes smaller than the elementary atomic modes [32][33][34] . Reducing further the integration volume only leads to an increase of the statistical uncertainty.…”

Section: Supplementary Materialsmentioning

confidence: 99%

An atomic Hong-Ou-Mandel experiment

Aspect

2014

Latin America Optics and Photonics Conference

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Quantum mechanics is a very successful and still intriguing theory, introducing two major counter-intuitive concepts. Wave-particle duality means that objects normally described as particles, such as electrons, can also behave as waves, while entities primarily described as waves, such as light, can also behave as particles.This revolutionary idea nevertheless relies on notions borrowed from classical physics, either waves or particles evolving in our ordinary space-time. By contrast, entanglement leads to interferences between the amplitudes of multi-particle states, which happen in an abstract mathematical space and have no classical counterpart. This fundamental feature has been strikingly demonstrated by the violation of Bell's inequalities [1][2][3][4] . There is, however, a conceptually simpler situation in which the interference between two-particle amplitudes entails a behaviour impossible to describe by any classical model. It was realised in the Hong, Ou and Mandel (HOM) experiment 5 , in which two photons arriving simultaneously in the input channels of a beam-splitter always emerge together in one of the output channels. In this letter, we report on the realisation, with atoms, of a HOM experiment closely following the original protocol. This opens the prospect of testing Bell's inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics 6,7 , with an eye on theories of the quantum-to-classical transition [8][9][10][11] . Our work also demonstrates a new way to produce and benchmark twin-atom pairs 12,13 that may be of interest for quantum information processing 14 and quantum simulation 15 .1 arXiv:1501.03065v2 [quant-ph] 15 Jan 2015A pair of entangled particles is described by a state vector that cannot be factored as a product of two state vectors associated with each particle. Although entanglement does not require that the two particles be identical 2 , it arises naturally in systems of indistinguishable particles due to the symmetrisation of the state. A remarkable illustration is the HOM experiment, in which two photons enter in the two input channels of a beam-splitter and one measures the correlation between the signals produced by photon counters placed at the two output channels. A joint detection at these detectors arises from two possible processes: either both photons are transmitted by the beam-splitter or both are reflected (Fig. 1c). If the two photons are indistinguishable, both processes lead to the same final quantum state and the probability of joint detection results from the addition of their amplitudes. Because of elementary properties of the beam-splitter, these amplitudes have same modulus but opposite signs, thus their sum vanishes and so also the probability of joint detection (Refs. [16,17] and Methods). In fact, to be fully indistinguishable, not only must the photons have the same energy and polarisation, but their final spatio-temporal modes must be identical. In the HOM experiment, it means that the t...

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Quantum noise in multipixel image processing

Cited by 81 publications

References 16 publications

Continuous-variable spatial entanglement for bright optical beams

Continuous-variable spatial entanglement for bright optical beams

Quantum fluctuations in the image of a Bose gas

An atomic Hong-Ou-Mandel experiment

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