Efficient High-Dimensional Entanglement Imaging with a Compressive-Sensing Double-Pixel Camera

Howland, Gregory A.; Howell, John C.

doi:10.1103/physrevx.3.011013

Cited by 67 publications

(91 citation statements)

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“…Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement 1,2 , and a test of the Einstein-Podolsky-Rosen (EPR) paradox 3 in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatio-temporal behavior 4 .…”

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confidence: 99%

“…an acquisition time of 4 seconds and a computation time that scales also in seconds since cross correlations are computed using FFT algorithms. This should be compared to days for raster scanning, or hours for compressivesensing 1 . Because of the experimental anisotropy, the dimensionality of entanglement, or Schmidt number K, can be assessed as the square root of the product of the paradox degrees in each direction: K = √ 594 × 85 = 225.…”

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confidence: 99%

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Einstein-Podolsky-Rosen Paradox in Twin Images

2014

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Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement 1,2 , and a test of the Einstein-Podolsky-Rosen (EPR) paradox 3 in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatio-temporal behavior 4 . Here, we record on two separate electron-multiplying charge coupled devices (EMCCD) cameras twin images of the entire flux of spontaneous down-conversion. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane) 5 . We report the highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom 6,7 or resolution cells 8 , of the images.In 1935, Einstein, Podolsky and Rosen (EPR) showed that quantum mechanics predicts that entangled particles could have both perfectly correlated positions and momenta, in contradiction with the so-called local realism where two distant particles should be treated as two different systems. Though the original intention of EPR was to show that quantum mechanics is not complete, the standard present view is that entangled particles do experience nonlocal correlations 9,10 . It can be shown that the spatial extent of these correlations corresponds to the size of a spatial unit of information, or mode, offering the possibility of detecting high dimensional entanglement in an image with a sufficient number of resolution cells 2,4 . However, in most experiments the use of single photon detectors and coincidence counting leads to the detection of a very few part of selected photons, generating a sampling loophole in fundamental demonstrations. High sensitivity array detectors have been used outside the single photoncounting regime in order to witness the quantum feature of light, showing the possibility of achieving larger signal-tonoise ratio than in classical imaging 11,12 . However, the EPR paradox is intimately connected to the particle character of light and its detection should involve single photon imaging, possible either with intensified charge coupled devices (ICCD) or, more recently, EMCCDs 13 . ICCDs exhibit a lower noise but have also a lower quantum efficiency than EMCCDs and a more extended spatial impulse response. ICCD are therefore convenient to isolate pairs of entangled photons 14 , as shown in a recent experiment: an ICCD triggered by a single photon detector was used to detect heralded photons in various spatial modes 15 .On the other hand, because of their higher quantum efficiency EMCCDs allow efficient detection of quantum correlations in images, as demonstrated some years ago by measuring sub-shot-noise correlations in far-field images of spontaneous parametric down-conversion (SPDC) 16,17 . More recently, two experiments intended to achieve the demonstra...

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confidence: 99%

Einstein-Podolsky-Rosen Paradox in Twin Images

2014

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“…The effect of nonperfect detection probability p d < 1 on the measured intensity correlation (22) can be incorporated by multiplying the joint (P ij ) and marginals (P i and P j ) detection probabilities of the photon pair by p 2 d and p d , respectively. The probability to detect a photon pair is given by p 2 d , while the probabilities of detecting only one or none of the photons from a pair is 2p d (1 − p d ) and (1 − p d ) 2 , respectively.…”

Section: E Effect Of Reduced Detection Probabilitymentioning

confidence: 99%

“…Nevertheless, as the noise level in these single-photon sensitive cameras is still much higher than in single-photon avalanche diodes, coincidence measurements using these cameras suffer from a much higher background than in the traditional scanning methods. Alternative approaches for measuring intensity correlations based on a digital micro-mirror array [21,22] or a time multiplexed fiber array [23,24] used in conjunction with a single-element detector have also recently been implemented.…”

Section: Introductionmentioning

confidence: 99%

Optimizing the use of detector arrays for measuring intensity correlations of photon pairs

et al. 2013

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Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyze the measurement of intensity correlations using multielement detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximizes the visibility of the two-photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying charge-coupled device camera, finding excellent agreement with the theoretical analysis.

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“…In this Letter, we introduce a method which combines the benefits of direct measurement with a novel computational technique known as compressive sensing [17][18][19][20][21][22]. Utilizing our approach, the wavefunction of a highdimensional state can be estimated with a high fidelity using much fewer number of measurements than a simple direct measurement approach.…”

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Compressive Direct Measurement of the Quantum Wave Function

et al. 2014

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The direct measurement of a complex wavefunction has been recently realized by using weakvalues. In this paper, we introduce a method that exploits sparsity for compressive measurement of the transverse spatial wavefunction of photons. The procedure involves a weak measurement in random projection operators in the spatial domain followed by a post-selection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate measurement of a 19200 dimensional state; a task that would require an unfeasibly large acquiring time with the conventional direct measurement technique.

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Efficient High-Dimensional Entanglement Imaging with a Compressive-Sensing Double-Pixel Camera

Cited by 67 publications

References 50 publications

Einstein-Podolsky-Rosen Paradox in Twin Images

Einstein-Podolsky-Rosen Paradox in Twin Images

Optimizing the use of detector arrays for measuring intensity correlations of photon pairs

Compressive Direct Measurement of the Quantum Wave Function

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