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REVIEW 4 major objections 6 minor 200 references

Advances in Position-Momentum Entanglement: A Versatile Tool for Quantum Technologies

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This review argues that position-momentum entanglement has advanced into a practical high-dimensional resource, with measurements as fast as 140 seconds for 48-dimensional certification and imaging applications that distill…

desk verdict A useful orientation review of position-momentum entanglement that needs a correction pass before it can be trusted as a reference; worth sending to a serious referee. read the letter →

arxiv 2505.22265 v2 pith:3VODXA4A submitted 2025-05-28 quant-ph

Satyajeet Patil , Sebastian Töpfer , Rajshree Swarnkar , Sergio Tovar-Perez , Jonas Moos , Jorge Fuenzalida , Markus Gräfe This is my paper
classification quant-ph
keywords spatialentanglementposition-momentumspontaneousparametricdown-conversionEPRcriterionquantumimagingSchmidtnumbersingle-photonavalanchediodecamerapumpcoherence
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review argues that position-momentum entanglement from spontaneous parametric down-conversion (SPDC) has matured from a test of the Einstein-Podolsky-Rosen paradox into a practical, high-dimensional resource for quantum technologies. It assembles the evidence across three fronts: generation of spatially entangled photon pairs in nonlinear crystals, measurement techniques that certify and quantify the entanglement, and applications spanning quantum imaging, communication, and metrology. The unifying claim is that the degree and type of entanglement can be engineered by choosing crystal parameters and the pump beam's spatial profile and coherence, making the resource tunable for specific tasks.

What carries the argument

The load-bearing object is the biphoton mode function Φ(ks, ki, z) at the crystal output, which the review approximates as a product of two Gaussians in the sum and difference of the transverse wavevectors (Eq. 9). This double-Gaussian form makes the position correlation width σ− depend only on crystal length and pump wavelength (Eq. 10), and the momentum correlation width σ+ depend inversely on the pump waist (Eq. 11), allowing the EPR variance product, the Schmidt number, and the joint probability distribution to be predicted directly from source parameters. The same structure is used throughout to explain how pump shaping and partial coherence modify the correlations.

What would settle it

Measure the EPR variance product and the Schmidt number for a sweep of crystal lengths and pump waists, and compare against the Gaussian-approximation formulas (Eqs. 10–11) and a full numerical sinc model; a systematic deviation that grows where the Gaussian is poorest would show the quantitative backbone does not hold.

Watch

Extended reading notes

Core claim

The paper's central claim is that position-momentum entanglement is a genuinely high-dimensional, continuous-variable resource whose practical exploitation is now limited less by sources than by measurement speed and propagation losses. The review documents EPR variance products as small as 0.01 ℏ² with slit-based detection, camera-based certification of entanglement in up to 48 dimensions within 140 seconds using SPAD arrays, and imaging demonstrations that distill quantum images from classical stray light, double the effective pixel resolution, and hide images inside correlation functions. It also surveys how the entanglement degrades when pump spatial coherence is reduced and how it can be shaped by elliptical or Bessel-Gaussian pumps, and it highlights the counter-intuitive result that angle-OAM entanglement, unlike position-momentum entanglement, can revive during free-space propagation.

Load-bearing premise

The quantitative backbone of the review is the replacement of the SPDC phase-matching sinc function by a Gaussian with adjustment parameter α=0.455; if that approximation is not faithful across the parameter regimes described, the reported EPR variances and Schmidt numbers derived from it could be systematically wrong.

Editorial extensions

If this is right

  • Camera-based correlation measurements with SPAD arrays cut acquisition time from hours to minutes, making high-dimensional entanglement certification fast enough for real-world quality control.
  • Reducing the spatial coherence of the pump weakens momentum anti-correlation while leaving position correlation intact, providing a controlled knob to tune entanglement up to a classical limit.
  • Elliptical pump beams can preserve entanglement along one transverse axis while erasing it along the other, enabling directional entanglement manipulation.
  • Position-momentum entanglement decays rapidly with free-space propagation, while angle-OAM entanglement can revive, guiding which spatial basis to use for long-distance links.
  • The transfer of the pump angular spectrum into the SPDC correlations lets one hide arbitrary amplitude or phase objects inside the correlation image while the intensity image stays uniform.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the double-Gaussian approximation is replaced by a more careful treatment of the sinc phase-matching tails, the EPR variances and Schmidt numbers for short crystals or tightly focused pumps may shift enough to matter for quantitative metrology protocols.
  • The pump-to-correlation transfer demonstrated for images suggests that structured pump beams could be used as a classical control channel to program the effective Hilbert-space dimension of the entangled state in real time.
  • The revival of angle-OAM entanglement in propagation hints that hybrid position-momentum and angle-OAM encoding could route information across different distance regimes in a future quantum network.
  • Combining the SPAD-based fast certification with machine-learned reconstruction of joint probability distributions could push high-dimensional entanglement certification beyond 48 dimensions without longer acquisition times.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript is a review of position-momentum entanglement generated by spontaneous parametric down-conversion (SPDC), organized into generation theory, measurement techniques, coherence and pump-shaping effects, propagation, and applications in imaging. The central thesis is that position-momentum entanglement has matured into a practical high-dimensional resource for quantum technologies. The review uses a double-Gaussian model of the biphoton amplitude as its quantitative backbone and surveys camera-based certification methods (EMCCD and SPAD arrays), cross-spectral-density measurements, and imaging demonstrations such as ghost imaging, image distillation, and pixel super-resolution.

Significance. If the quantitative statements are corrected, this review could serve as a useful entry point for researchers; the taxonomy of estimation/certification/quantification, the compilation of experimental EPR products, and the discussion of partial-coherence and beam-shaping control are informative. The paper is not an original derivation and does not include machine-checked proofs, but it does aggregate a large body of recent literature and explicitly highlights practical trade-offs such as acquisition time. However, the current text contains a concrete formula error, an inconsistent quantitative claim, and an unvalidated extension of the Gaussian model, so the supporting quantitative narrative needs revision before the review can be relied upon.

major comments (4)
  1. [III.D, Eq. (16)] In the definition of the joint probability distribution Γ(r_i,r_j), the second term sums over all N × N frame pairs (l′,l), including l′ = l, whereas the text states that the second term contains only accidental coincidences from different frames. As written, the same-frame intensity correlation is subtracted along with the accidental correlations, biasing the estimated JPD. The sum must be restricted to l′ ≠ l (or to explicitly non-overlapping frames) to isolate true coincidences.
  2. [III.D and IV] The confidence level for the EPR violation obtained with the SPAD camera is reported as 227σ in Section III.D and as 277σ in Section IV. Both statements cite the same experiment [13]. The authors should reconcile these numbers with the source and use one consistent value; as written, a reader cannot tell which quantitative claim is correct.
  3. [II, V, and VII] The double-Gaussian approximation with α=0.455 is introduced in Eq. (10) under collinear phase matching, but the same σ− is then used in the partially coherent model of Eq. (29) and Eq. (32), in the propagation expression Eq. (39), and as the reference for several experimental comparisons. The review provides no validation of the Gaussian replacement of the sinc phase-matching function for non-collinear geometries, different phase-matching types, or partially coherent pumps. Since the reported EPR products and Schmidt numbers inherit this approximation, the authors should either restrict the model to its validated regime or provide a quantitative comparison with the sinc model (or with data) for each regime in which it is applied.
  4. [References [19] and [28]] The reference list contains two entries that are not in finished form: Ref. [19] includes editorial notes ('review paper. 27 pages, 9 figures, 250+ references. Comments welcome!') and Ref. [28] names 'J. Doe and J. Smith' as authors. A review's reference list is a load-bearing part of the manuscript; these entries must be replaced with the actual bibliographic data or removed.
minor comments (6)
  1. [I.D] The name 'Drudmund' should be 'Drummond'.
  2. [III.D] The phrase 'totatl number of frames' should be 'total number of frames'.
  3. [V, Eq. (29)] The surrounding text defines the beam waist as w while the equation uses w_p; the notation should be made consistent.
  4. [VII] The section heading reads 'PROP AGA TION' and should be 'PROPAGATION'.
  5. [VII] The text refers to figure 30(c)-(f) for JPD and conditional-uncertainty evolution, but those panels appear in figure 29; the cross-references should be corrected.
  6. [VIII.D] The phrase 'Author’s approach' should be 'The authors’ approach'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: this review compiles external experimental results and uses the standard double-Gaussian approximation as a modeling tool, not as a fitted prediction.

full rationale

This is a review article, not a derivation with fitted parameters or novel predictions. The quantitative framework is the double-Gaussian approximation of the SPDC biphoton amplitude (Eqs. 8-12), with alpha = 0.455 in Eq. (10). That parameter is an externally established analytical approximation from the literature, not calibrated in this paper, and it is applied to known experimental configurations rather than used to generate predictions that are then fed back into the model. The comparisons to experimental values, for example in Section III.E, use theoretical expressions derived from this model and external experiments; no quantity is fitted to a subset of data and then renamed a prediction. The survey cites several works by the authors themselves (e.g., refs. 17, 45, 47, 48, 103, 161, 165, 166, 168, 169, 172), but these citations point to independent experimental or numerical results and are not used as the sole justification of the review's central claims, nor to exclude alternative approaches. No uniqueness theorem from the authors' prior work is invoked, and no ansatz is smuggled in via self-citation. The possible concern that the double-Gaussian approximation might be applied beyond its validated collinear regime is a question of model fidelity and correctness, not circularity, because the review does not derive its conclusions from the same data it claims to predict. The central assertion that position-momentum entanglement is a versatile resource is supported by a broad body of externally reported experiments and remains independently falsifiable. Therefore the paper exhibits no significant circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The review's quantitative formulas rest on the standard Gaussian model of SPDC and on camera-based correlation measurements. These are assumptions inherited from the cited literature, not derived in this paper. The paper introduces no new free parameters, axioms, or entities beyond quoting existing ones.

free parameters (1)
  • alpha (Gaussian approximation parameter for phase-matching sinc) = 0.455
    Introduced in Eq. (10) to approximate the sinc function in the SPDC mode function. It sets the position correlation width and is used in subsequent calculations of EPR criteria and coherence-dependent entanglement.
assumptions (4)
  • domain assumption The SPDC biphoton state can be represented by the mode function in Eqs. (7)-(8) under collinear phase matching and paraxial approximation.
    This is the standard starting point for the review's theoretical background, taken from cited literature such as Refs. [89, 98, 99].
  • ad hoc to paper The phase-matching sinc function can be approximated by a Gaussian with alpha = 0.455.
    Used in Eq. (10) to derive the position correlation width; this is a fitting approximation rather than an exact identity.
  • domain assumption Intensity correlation measurements with camera arrays yield the joint probability distribution of the biphoton state when subtracting accidental coincidences.
    Underlies the experimental techniques in Section III.D and the JPD definitions in Eq. (16).
  • standard math The EPR criterion (Eq. 1) is a valid witness of entanglement for the states under consideration.
    A widely used criterion for continuous-variable entanglement, assumed valid throughout the review.

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Cite this review

Pith. "Pith review of Advances in Position-Momentum Entanglement: A Versatile Tool for Quantum Technologies." pith.science (2026). https://pith.science/paper/3VODXA4A

@misc{pith2026250522265,
  author       = {Pith},
  title        = {Pith review of: Advances in Position-Momentum Entanglement: A Versatile Tool for Quantum Technologies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3VODXA4A}},
  note         = {Machine review of arXiv:2505.22265}
}
read the original abstract

Position-momentum entanglement is a versatile high-dimensional resource in quantum optics. From fundamental tests of reality to applications in quantum technologies, spatial entanglement has experienced significant growth in recent years. In this review, we explore these advances, beginning with the generation of spatial entanglement, followed by various types of measurements for certifying entanglement, and concluding with different quantum-based applications. We conclude the review with a discussion and outlook of the field.

Figures

Figures reproduced from arXiv: 2505.22265 by the authors.

Figure 1
Figure 1. SPDC emission angles. In a SPDC process, a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Conservation relations of the (a) energy and (b) wavevectors kp = ks + ki . was first theoretically predicted by Louisell et al in 1961 [54] who modeled it as two oscillators coupled via a time-dependent reactance. Later, Giallorenzi et al [55] explained SPDC as the scattering process in which a pump photon is transformed into a photon-pair because of the non-linear polarization. It’s first experimental observation … view at source ↗
Figure 3
Figure 3. Amplitude and phase-matching conditions. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (31 more)
Figure 4
Figure 4. Figure 4: Experimental setup: (a) to measure position [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 7
Figure 7. Figure 7: Illustration of the process by which a single [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 6
Figure 6. Figure 6: Fedorov ratio measured between far field and [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: 4-f imaging configuration to measure position/near-field correlation using EMCCD [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: 2-f imaging configuration to measure momentum/far-field correlation using EMCCD. To measure correlations of all photon pairs in a frame at once, one can sum the frame along rows or columns as shown in figure 10(a). Summing along rows adds all grey-scale values in turns…
Figure 11
Figure 11. Figure 11: Illustration of the process where an image is [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 12
Figure 12. Figure 12: (a) Experimental setup for measuring position cross-spectral density function. (b) Interferogram recorded at δc = 0 with the configuration in (a). (c) Interferogram recorded at δc = π with the configuration in (a). (d) Difference intensity image ∆I(˜xs, y˜s). (e) Expe…
Figure 13
Figure 13. Figure 13: Experimental setup for the characterization [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]
Figure 14
Figure 14. Figure 14: Position and momentum correlations of SPDC using laser and LED pumping. (a), and (c) shows the coincidence rates that are recorded in the near field to obtain position distributions. (b) and (d) are the coincidence rates measured in the far field for momentum distribu…
Figure 16
Figure 16. Figure 16: Momentum anti-correlation, position correlation, and entanglement relationship for pump beams with varying coherence lengths. Image reference [16]. losing strength [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]
Figure 17
Figure 17. Figure 17: Setup of a pump beam with partial spatial [PITH_FULL_IMAGE:figures/full_fig_p013_17.png]
Figure 19
Figure 19. Figure 19: (b) shows how the Schmidt number K varies as a function of decreasing coherence length of the pump beam [PITH_FULL_IMAGE:figures/full_fig_p013_19.png]
Figure 20
Figure 20. Figure 20: Computed values of the parameters influencing the spatial entanglement and correlation of SPDC as the coherence length of the pump beam is reduced by adding diffusive layers. Image reference [142]. VI. ENGINEERING JOINT PROBABILITY DISTRIBUTION To tailor the shape of …
Figure 21
Figure 21. Figure 21: Experimental setup to study the position-momentum entanglement generated from an elliptical pump beam using second-order nonlinear crystal. CL1 & CL2: cylindrical lenses; NLC: nonlinear crystal (BBO); BPF: band-pass filter. (a) Near-field configuration, (b) Far-field …
Figure 24
Figure 24. Figure 24: (a) Intensity distribution of the pump beam [PITH_FULL_IMAGE:figures/full_fig_p015_24.png]
Figure 22
Figure 22. Figure 22: Intensity distribution of the pump beam and [PITH_FULL_IMAGE:figures/full_fig_p015_22.png]
Figure 23
Figure 23. Figure 23: The variation of γx (blue-circle) and γy (red-circle) against the asymmetry factor β. Continuous traces, blue and red correspond to theoretical variation of γx and γy with β, respectively. (For interpretation of the colors in the figure(s), the reader is referred to t…
Figure 27
Figure 27. Figure 27: (a) The JPD of photon pairs in wave-vector [PITH_FULL_IMAGE:figures/full_fig_p016_27.png]
Figure 25
Figure 25. Figure 25: Schematic of experimental setup. The SLM [PITH_FULL_IMAGE:figures/full_fig_p016_25.png]
Figure 26
Figure 26. Figure 26: The JPD of the photon-pairs in the sum-coordinate basis shaped in (a) Bessel-Gaussian for the pump beam shaped as perfect vortex, shown in inlet image, (b) perfect vortex for the pump beam shaped as Bessel-Gaussian, shown in inlet image, (c) checker-board for the pump…
Figure 28
Figure 28. Figure 28: (a) Schematic of the experimental setup for [PITH_FULL_IMAGE:figures/full_fig_p017_28.png]
Figure 31
Figure 31. Figure 31: First setup for ghost imaging. Taken from [PITH_FULL_IMAGE:figures/full_fig_p018_31.png]
Figure 30
Figure 30. Figure 30: Propagation of entanglement in the position-momentum and angle-OAM Bases (a) Conditional position-momentum uncertainty product, ∆(ys | yi ; z)∆(pys | pyi ; z), as a function of the propagation distance z. The solid dots represent experimental results, while the solid …
Figure 32
Figure 32. Figure 32: (a) Aperture that serves as an object. (b) [PITH_FULL_IMAGE:figures/full_fig_p019_32.png]
Figure 33
Figure 33. Figure 33: Setup for computational ghost imaging with [PITH_FULL_IMAGE:figures/full_fig_p019_33.png]
Figure 34
Figure 34. Figure 34: Setup for quantum image distillation and the [PITH_FULL_IMAGE:figures/full_fig_p019_34.png]
Figure 35
Figure 35. Figure 35: (a) Direct intensity image taken by the camera. (b) Image produced by measuring the correlation function, revealing the object in the quantum arm. (c) Image of the object in the classical arm obtained by subtracting the correlation image from the direct intensity imag…
Figure 37
Figure 37. Figure 37: (a) Experimental Setup for pixel super-resolution. (b) Intensity Image, (b) JPD diagonal image and (d) sum-coordinate projection of the JPD with a pixel pitch of ∆ = 32 µm. (e) Intensity image where a camera with half the pixel pitch is used compared to (b). (f) line …
Figure 36
Figure 36. Figure 36: (a) SNRs measured at different average classical to quantum light intensity ratios Icl/Iqu and the expected SNRs from theory. (b) Intensity image by both classical and quantum light. (c), (d) and (e) show the negative-coordinate projections of Γ at Icl/Iqu = 0, Icl/Iq…
Figure 39
Figure 39. Figure 39: Correlation images with (a) a sleeping cat-shaped mask as object and (b) an additional standing cat mask between the lenses f1 and f2. The direct intensity images are located in the bottom left corner in each case. Taken from [95]. IX. SUMMARY AND PERSPECTIVES Spatial…
Figure 38
Figure 38. Figure 38: (a) Experimental setup for hiding images in [PITH_FULL_IMAGE:figures/full_fig_p021_38.png]

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Works this paper leans on

200 extracted references · 71 canonical work pages

  1. [27]

    Ali Khan and J

    I. Ali Khan and J. C. Howell, Experimental demon- stration of high two-photon time-energy entanglement, Phys. Rev. A 73, 031801 (2006)

    2006

  2. [13]

    Y. Liu, X. Yuan, M.-H. Li, W. Zhang, Q. Zhao, J. Zhong, Y. Cao, Y.-H. Li, L.-K. Chen, H. Li, T. Peng, Y.-A. Chen, C.-Z. Peng, S.-C. Shi, Z. Wang, L. You, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, High-speed device-independent quantum random number genera- tion without a detection loophole, Phys. Rev. Lett. 120, 010503 (2018)

    2018

  3. [19]

    Zhang, R

    W. Zhang, R. Fickler, E. Giese, L. Chen, and R. W. Boyd, Influence of pump coherence on the generation of position-momentum entanglement in optical parametric down-conversion, Opt. Express 27, 20745 (2019). 23

    2019

  4. [28]

    L. K. Shalm, D. R. Hamel, Z. Yan, C. Simon, K. J. Resch, and T. Jennewein, Three-photon energy–time entanglement, Nature Physics 9, 19 (2013)

    2013

  5. [1]

    − |ρs + ρi|2 4w(z)2 # × exp

    Beam shaping In another reference [94], a generalized study of spatial shaping of the pump has been reported. The spatial profile of the pump beam is modified using a spatial light modulator (SLM). The setup for the experiment is shown in the figure 26. A continuous wave laser illuminates the SLM that tailor its beam profile and 15 Figure 22: Intensity di...

    1995

  6. [2]

    Schr¨ odinger, Discussion of probability relations be- tween separated systems, Mathematical Proceedings of the Cambridge Philosophical Society 31, 555–563 (1935)

    E. Schr¨ odinger, Discussion of probability relations be- tween separated systems, Mathematical Proceedings of the Cambridge Philosophical Society 31, 555–563 (1935)

    1935

  7. [3]

    engi- neered

    Such projection retrieves the image of the object with pixel resolution increased by P + i+j+ = NXX i=1 NYX j=1 Γ(i+−i)(j+−j)ij, (41) where, NX ×NY are the number of pixels of the illumi- nated region, P + is the sum-coordinate projection of the JPD and ( i+, j+) sum-coordinate pixel indices. Because of the pixel-super resolution, one can see that the spu...

  8. [4]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Can quantum- mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935)

    1935

Show all 200 references
  1. [5]

    B. S. Cirel’son, Quantum generalizations of bell’s in- equality, Letters in Mathematical Physics 4, 93 (1980)

    1980

  2. [6]

    Bohm and Y

    D. Bohm and Y. Aharonov, Discussion of experimental proof for the paradox of einstein, rosen, and podolsky, Phys. Rev. 108, 1070 (1957)

    1957

  3. [7]

    J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika 1, 195 (1964)

    1964

  4. [8]

    Bouwmeester, J.-W

    D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. We- infurter, and A. Zeilinger, Experimental quantum tele- portation, Nature 390, 575 (1997)

    1997

  5. [9]

    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969)

    1969

  6. [10]

    A. K. Ekert, Quantum cryptography based on bell’s the- orem, Phys. Rev. Lett. 67, 661 (1991)

    1991

  7. [11]

    J. C. F. Matthews, X.-Q. Zhou, H. Cable, P. J. Shad- bolt, D. J. Saunders, G. A. Durkin, G. J. Pryde, and J. L. O’Brien, Towards practical quantum metrology with photon counting, NPJ Quantum Information 2, 16023 (2016)

    2016

  8. [12]

    J. E. Jacak, W. A. Jacak, W. A. Donderowicz, and L. Jacak, Quantum random number generators with en- tanglement for public randomness testing, Scientific Re- ports 10, 164 (2020)

    2020

  9. [14]

    Leach, R

    J. Leach, R. E. Warburton, D. G. Ireland, F. Izdebski, S. M. Barnett, A. M. Yao, G. S. Buller, and M. J. Pad- gett, Quantum correlations in position, momentum, and intermediate bases for a full optical field of view, Phys. Rev. A 85, 013827 (2012)

    2012

  10. [15]

    J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, Realization of the einstein-podolsky-rosen para- dox using momentum- and position-entangled photons from spontaneous parametric down conversion, Phys. Rev. Lett. 92, 210403 (2004)

    2004

  11. [16]

    Defienne, T

    H. Defienne, T. Reichert, Q. Sun, R. S. Aspden, T. Schneider, K. Lee, R. Fickler, G. Leuchs, R. W. Boyd, and C. Silberhorn, Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera, npj Quantum Information 6, 1 (2020)

    2020

  12. [17]

    Patil, S

    S. Patil, S. Prabhakar, A. Biswas, A. Kumar, and R. P. Singh, Anisotropic spatial entanglement, Physics Let- ters A 457, 128583 (2023)

    2023

  13. [18]

    Achatz, E

    L. Achatz, E. Ortega, K. Dovzhik, R. F. Shiozaki, J. Fuenzalida, S. Wengerowsky, M. Bohmann, and R. Ursin, Certifying position-momentum entanglement at telecommunication wavelengths, Journal of Optics 22, 125201 (2020)

    2020

  14. [21]

    J. D. Franson, Bell inequality for position and time, Phys. Rev. Lett. 62, 2205 (1989)

    1989

  15. [22]

    G. B. Xavier, J.- . Larsson, P. Villoresi, G. Val- lone, and A. Cabello, Energy-time and time-bin en- tanglement: past, present and future, arXiv preprint arXiv:2503.14675 (2025), review paper. 27 pages, 9 fig- ures, 250+ references. Comments welcome!

    2025 arXiv

  16. [23]

    P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, High- visibility interference in a bell-inequality experiment for energy and time, Phys. Rev. A 47, R2472 (1993)

    1993

  17. [24]

    Ali-Khan, C

    I. Ali-Khan, C. J. Broadbent, and J. C. Howell, Large- alphabet quantum key distribution using energy-time entangled bipartite states, Phys. Rev. Lett. 98, 060503 (2007)

    2007

  18. [25]

    D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, Postselection-free energy-time entanglement, Phys. Rev. A 54, R1 (1996)

    1996

  19. [26]

    Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Quantum entanglement and squeezing of the quadrature difference of bright light fields, Physical Review Letters 68, 3663 (1992)

    1992

  20. [29]

    W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, Experimental investigation of criteria for contin- uous variable entanglement, Phys. Rev. Lett.90, 043601 (2003)

    2003

  21. [30]

    Doe and J

    J. Doe and J. Smith, Quadrature entanglement in the microwave domain with a phase locking protocol, Phys- ical Review Letters 130, 060501 (2023)

    2023

  22. [31]

    Furusawa, J

    A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Experimental re- alization of spatially separated entanglement with con- tinuous variables using laser pulse trains, Science 282, 706 (1998)

    1998

  23. [32]

    Leach, B

    J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, Quan- tum correlations in optical angle–orbital angular momentum variables, Science 329, 662 (2010), https://www.science.org/doi/pdf/10.1126/scien...

    2010 doi

  24. [33]

    Edgar, D

    M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Pad- gett, Imaging high-dimensional spatial entanglement with a camera, Nature Communications 3, 984 (2012)

    2012

  25. [34]

    Moreau, F

    P.-A. Moreau, F. Devaux, and E. Lantz, Einstein- podolsky-rosen paradox in twin images, Phys. Rev. Lett. 113, 160401 (2014)

    2014

  26. [35]

    Giedke, B

    G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, Entanglement criteria for all bipartite gaussian states, Phys. Rev. Lett. 87, 167904 (2001)

    2001

  27. [36]

    A. E. Rastegin, R´ enyi formulation of entanglement cri- teria for continuous variables, Phys. Rev. A 95, 042334 (2017)

    2017

  28. [37]

    Saboia, F

    A. Saboia, F. Toscano, and S. P. Walborn, Family of continuous-variable entanglement criteria using general entropy functions, Phys. Rev. A 83, 032307 (2011)

    2011

  29. [38]

    S. L. Braunstein and H. J. Kimble, Teleportation of con- tinuous quantum variables, Phys. Rev. Lett. 80, 869 (1998)

    1998

  30. [39]

    Simon, Peres-horodecki separability criterion for con- tinuous variable systems, Phys

    R. Simon, Peres-horodecki separability criterion for con- tinuous variable systems, Phys. Rev. Lett. 84, 2726 (2000)

    2000

  31. [40]

    Scarfe, Y

    L. Scarfe, Y. Zhang, and E. Karimi, Spatial-mode quan- tum cryptography in a 545-dimensional hilbert space (2025), arXiv:2503.22058 [quant-ph]

    2025

  32. [41]

    used a SPAD camera proving their worth in various fields including quantum imaging in a robust scheme against stray light. C. Pixel-super-resolution imaging Due to the presence of strong position correlations in photon pairs, this can be leveraged to achieve pixel super-resolu...

  33. [42]

    Defienne, M

    H. Defienne, M. Reichert, J. W. Fleis- cher, and D. Faccio, Quantum image distil- lation, Science Advances 5, eaax0307 (2019), https://www.science.org/doi/pdf/10.1126/sciadv.aax0307

    2019 doi

  34. [44]

    Defienne, J

    H. Defienne, J. Zhao, E. Charbon, and D. Faccio, Full- field quantum imaging with a single-photon avalanche diode camera, Phys. Rev. A 103, 042608 (2021)

    2021

  35. [45]

    Reichert, H

    M. Reichert, H. Defienne, X. Sun, and J. W. Fleis- cher, Biphoton transmission through non-unitary ob- jects, Journal of Optics 19, 034013 (2017)

    2017

  36. [46]

    Ndagano and D

    B. Ndagano and D. Faccio, Quantum microscopy based on hong–ou–mandel interference, Nature Communica- tions 13, 1215 (2022)

    2022

  37. [47]

    Moreau, E

    P.-A. Moreau, E. Toninelli, P. A. Morris, R. S. Aspden, T. Gregory, G. Spalding, R. W. Boyd, and M. J. Pad- gett, Resolution limits of quantum ghost imaging, Opt. Express 26, 7528 (2018)

    2018

  38. [48]

    Fuenzalida, A

    J. Fuenzalida, A. Hochrainer, G. B. Lemos, E. A. Or- tega, R. Lapkiewicz, M. Lahiri, and A. Zeilinger, Res- olution of quantum imaging with undetected photons, Quantum 6, 646 (2022)

    2022

  39. [49]

    Viswanathan, G

    B. Viswanathan, G. Barreto Lemos, and M. Lahiri, Resolution limit in quantum imaging with undetected photons using position correlations, Optics Express 29, 38185 (2021)

    2021

  40. [50]

    A. Vega, E. A. Santos, J. Fuenzalida, M. Gilaberte Bas- set, T. Pertsch, M. Gr¨ afe, S. Saravi, and F. Setzp- fandt, Fundamental resolution limit of quantum imaging with undetected photons, Physical Review Research 4, 033252 (2022)

    2022

  41. [51]

    Gilaberte Basset, R

    M. Gilaberte Basset, R. Sondenheimer, J. Fuenzalida, A. Vega, S. T¨ opfer, E. A. Santos, S. Saravi, F. Set- zpfandt, F. Steinlechner, and M. Gr¨ afe, Experimental analysis of image resolution of quantum imaging with undetected light through position correlations, Physical Revi...

    2023

  42. [52]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature Photonics 5, 222 (2011)

    2011

  43. [53]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006)

    2006

  44. [54]

    Aspect, P

    A. Aspect, P. Grangier, and G. Roger, Experimental tests of realistic local theories via bell’s theorem, Phys. Rev. Lett. 47, 460 (1981)

    1981

  45. [55]

    Aspect, J

    A. Aspect, J. Dalibard, and G. Roger, Experimental test of bell’s inequalities using time-varying analyzers, Phys. Rev. Lett. 49, 1804 (1982). 24

    1982

  46. [56]

    C. A. Kocher and E. D. Commins, Polarization corre- lation of photons emitted in an atomic cascade, Phys. Rev. Lett. 18, 575 (1967)

    1967

  47. [57]

    W. H. Louisell, A. Yariv, and A. E. Siegman, Quantum fluctuations and noise in parametric processes. i., Phys. Rev. 124, 1646 (1961)

    1961

  48. [58]

    T. G. Giallorenzi and C. L. Tang, Quantum theory of spontaneous parametric scattering of intense light, Phys. Rev. 166, 225 (1968)

    1968

  49. [59]

    S. E. Harris, M. K. Oshman, and R. L. Byer, Obser- vation of tunable optical parametric fluorescence, Phys. Rev. Lett. 18, 732 (1967)

    1967

  50. [60]

    D. C. Burnham and D. L. Weinberg, Observation of simultaneity in parametric production of optical photon pairs, Phys. Rev. Lett. 25, 84 (1970)

    1970

  51. [61]

    Hanbury Brown and R

    R. Hanbury Brown and R. Q. Twiss, A test of a new type of stellar interferometer on sirius, Nature178, 1046 (1956)

    1956

  52. [62]

    R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008)

    2008

  53. [63]

    M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, Theory of two-photon entanglement in type- ii optical parametric down-conversion, Phys. Rev. A 50, 5122 (1994)

    1994

  54. [64]

    P. G. Kwiat, P. H. Eberhard, A. M. Steinberg, and R. Y. Chiao, Proposal for a loophole-free bell inequality exper- iment, Phys. Rev. A 49, 3209 (1994)

    1994

  55. [65]

    P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, New high-intensity source of polarization-entangled photon pairs, Phys. Rev. Lett. 75, 4337 (1995)

    1995

  56. [66]

    P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, Ultrabright source of polarization- entangled photons, Phys. Rev. A 60, R773 (1999)

    1999

  57. [67]

    J. G. Rarity and P. R. Tapster, Experimental viola- tion of bell’s inequality based on phase and momentum, Phys. Rev. Lett. 64, 2495 (1990)

    1990

  58. [68]

    A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Entan- glement of the orbital angular momentum states of pho- tons, Nature 412, 313 (2001)

    2001

  59. [70]

    S. P. Walborn and C. H. Monken, Transverse spatial en- tanglement in parametric down-conversion, Phys. Rev. A 76, 062305 (2007)

    2007

  60. [71]

    J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Interactions between Light Waves in a Nonlin- ear Dielectric, Physical Review 127, 1918 (1962), pub- lisher: American Physical Society

    1962

  61. [72]

    Mattle, H

    K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, Dense coding in experimental quantum communication, Phys. Rev. Lett. 76, 4656 (1996)

    1996

  62. [73]

    C. H. Bennett, G. Brassard, and N. D. Mermin, Quan- tum cryptography without bell’s theorem, Phys. Rev. Lett. 68, 557 (1992)

    1992

  63. [74]

    W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature 299, 802 (1982)

    1982

  64. [75]

    R. A. Beth, Mechanical detection and measurement of the angular momentum of light, Phys. Rev. 50, 115 (1936)

    1936

  65. [76]

    Padgett, J

    M. Padgett, J. Courtial, and L. Allen, Light’s Orbital Angular Momentum, Physics Today 57, 35 (2004), https://pubs.aip.org/physicstoday/article- pdf/57/5/35/8317006/35 1 online.pdf

    2004

  66. [77]

    Molina-Terriza, J

    G. Molina-Terriza, J. P. Torres, and L. Torner, Twisted photons, Nature Physics 3, 305 (2007)

    2007

  67. [78]

    Brandt, M

    F. Brandt, M. Hiekkam¨ aki, F. Bouchard, M. Huber, and R. Fickler, High-dimensional quantum gates using full- field spatial modes of photons, Optica 7, 98 (2020)

    2020

  68. [79]

    Anwar, S

    A. Anwar, S. Prabhakar, and R. P. Singh, Size-invariant twisted optical modes for the efficient generation of higher-dimensional quantum states, J. Opt. Soc. Am. B 38, 2976 (2021)

    2021

  69. [80]

    Karimipour, A

    V. Karimipour, A. Bahraminasab, and S. Bagher- inezhad, Entanglement swapping of generalized cat states and secret sharing, Physical Review A 65, 042320 (2002)

    2002

  70. [81]

    Bechmann-Pasquinucci and A

    H. Bechmann-Pasquinucci and A. Peres, Quantum cryp- tography with 3-state systems, Physical Review Letters 85, 3313 (2000)

    2000

  71. [82]

    Molina-Terriza, J

    G. Molina-Terriza, J. P. Torres, and L. Torner, Manage- ment of the angular momentum of light: Preparation of photons in multidimensional vector states of angular momentum, Phys. Rev. Lett. 88, 013601 (2001)

    2001

  72. [83]

    Vaziri, G

    A. Vaziri, G. Weihs, and A. Zeilinger, Experimental two- photon, three-dimensional entanglement for quantum communication, Phys. Rev. Lett. 89, 240401 (2002)

    2002

  73. [84]

    J. P. Torres, Y. Deyanova, L. Torner, and G. Molina- Terriza, Preparation of engineered two-photon entan- gled states for multidimensional quantum information, Phys. Rev. A 67, 052313 (2003)

    2003

  74. [85]

    Anwar, N

    A. Anwar, N. Lal, S. Prabhakar, and R. P. Singh, Selec- tive tuning of hilbert spaces in states encoded with spa- tial modes of light, New Journal of Physics 22, 113020 (2020)

    2020

  75. [86]

    M. V. Jabir, A. Anwar, and G. K. Samanta, Controlling the bi-photon orbital angular momentum eigenmodes using asymmetric pump vortex beam, Journal of Optics 21, 055201 (2019)

    2019

  76. [87]

    M. D. Reid and P. D. Drummond, Quantum correlations of phase in nondegenerate parametric oscillation, Phys. Rev. Lett. 60, 2731 (1988)

    1988

  77. [88]

    Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Realization of the einstein-podolsky-rosen paradox for continuous variables, Phys. Rev. Lett. 68, 3663 (1992)

    1992

  78. [89]

    L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Insep- arability criterion for continuous variable systems, Phys. Rev. Lett. 84, 2722 (2000)

    2000

  79. [90]

    D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Observation of two-photon “ghost” interfer- ence and diffraction, Phys. Rev. Lett. 74, 3600 (1995)

    1995

  80. [91]

    T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Optical imaging by means of two-photon quantum entanglement, Phys. Rev. A52, R3429 (1995)

    1995

  81. [92]

    C. H. Monken, P. H. S. Ribeiro, and S. P´ adua, Trans- fer of angular spectrum and image formation in spon- taneous parametric down-conversion, Phys. Rev. A 57, 3123 (1998)

    1998

  82. [93]

    A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Demonstration of the com- plementarity of one- and two-photon interference, Phys. Rev. A 63, 063803 (2001)

    2001

  83. [94]

    S. P. Walborn, D. S. Lemelle, M. P. Almeida, and P. H. S. Ribeiro, Quantum key distribution with higher- order alphabets using spatially encoded qudits, Phys. Rev. Lett. 96, 090501 (2006). 25

    2006

  84. [95]

    S. P. Walborn, D. S. Lemelle, D. S. Tasca, and P. H. Souto Ribeiro, Schemes for quantum key distribution with higher-order alphabets using single-photon frac- tional fourier optics, Phys. Rev. A 77, 062323 (2008)

    2008

  85. [97]

    Boucher, H

    P. Boucher, H. Defienne, and S. Gigan, Engineering spatial correlations of entangled photon pairs by pump beam shaping, Opt. Lett. 46, 4200 (2021)

    2021

  86. [98]

    Verni` ere and H

    C. Verni` ere and H. Defienne, Hiding Images in Quan- tum Correlations, Physical Review Letters 133, 093601 (2024)

    2024

  87. [99]

    Reichert, X

    M. Reichert, X. Sun, and J. W. Fleischer, Quality of spa- tial entanglement propagation, Phys. Rev. A95, 063836 (2017)

    2017

  88. [100]

    Bhattacharjee, M

    A. Bhattacharjee, M. K. Joshi, S. Karan, J. Leach, and A. K. Jha, Propagation-induced revival of entanglement in the angle-oam bases, Science Advances 8, eabn7876 (2022), https://www.science.org/doi/pdf/10.1126/sciadv.abn7876

    2022 doi

  89. [102]

    D. S. Tasca, S. P. Walborn, P. H. Souto Ribeiro, F. Toscano, and P. Pellat-Finet, Propagation of trans- verse intensity correlations of a two-photon state, Phys. Rev. A 79, 033801 (2009)

    2009

  90. [103]

    Friis, G

    N. Friis, G. Vitagliano, M. Malik, and M. Huber, Entan- glement certification from theory to experiment, Nat. Rev. Phys. 1, 72 (2019)

    2019

  91. [104]

    Brambilla, A

    E. Brambilla, A. Gatti, M. Bache, and L. A. Lugiato, Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down- conversion, Phys. Rev. A 69, 023802 (2004)

    2004

  92. [105]

    Kviatkovsky, H

    I. Kviatkovsky, H. M. Chrzanowski, E. G. Avery, H. Bartolomaeus, and S. Ramelow, Microscopy with undetected photons in the mid-infrared, Sci. Adv. 6, eabd0264 (2020)

    2020

  93. [106]

    M. Hong, R. G´ omez, V. Flavio Gili, J. Fuenzalida, and M. Gr¨ afe, Polarization-entangled photon-pair source us- ing beam displacers and thin crystals, Opt. Lett. 49, 5467 (2024)

    2024

  94. [107]

    C. K. Law and J. H. Eberly, Analysis and interpretation of high transverse entanglement in optical parametric down conversion, Phys. Rev. Lett. 92, 127903 (2004)

    2004

  95. [109]

    E. A. Ortega, J. Fuenzalida, M. Selimovic, K. Dovzhik, L. Achatz, S. Wengerowsky, R. F. Shiozaki, S. P. Neu- mann, M. Bohmann, and R. Ursin, Spatial and spectral characterization of photon pairs at telecommunication wavelengths from type-0 spontaneous parametric down- conversi...

    2022

  96. [110]

    F. Just, A. Cavanna, M. V. Chekhova, and G. Leuchs, Transverse entanglement of biphotons, New J. Phys.15, 083015 (2013)

    2013

  97. [111]

    Brida, V

    G. Brida, V. Caricato, M. Fedorov, M. Genovese, M. Gramegna, and S. Kulik, Characterization of spec- tral entanglement of spontaneous parametric-down con- version biphotons in femtosecond pulsed regime, EPL 87, 64003 (2009)

    2009

  98. [112]

    M. V. Fedorov, M. A. Efremov, A. E. Kazakov, K. W. Chan, C. K. Law, and J. H. Eberly, Packet narrowing and quantum entanglement in photoionization and pho- todissociation, Phys. Rev. A 69, 052117 (2004)

    2004

  99. [113]

    K. W. Chan, J. P. Torres, and J. H. Eberly, Transverse entanglement migration in hilbert space, Phys. Rev. A 75, 050101 (2007)

    2007

  100. [114]

    Defienne, M

    H. Defienne, M. Reichert, and J. W. Fleischer, General model of photon-pair detection with an image sensor, Phys. Rev. Lett. 120, 203604 (2018)

    2018

  101. [115]

    Eckmann, B

    B. Eckmann, B. Bessire, M. Untern¨ ahrer, L. Gasparini, M. Perenzoni, and A. Stefanov, Characterization of space-momentum entangled photons with a time resolv- ing cmos spad array, Opt. Express 28, 31553 (2020)

    2020

  102. [116]

    Kundu, J

    S. Kundu, J. Szuniewicz, G. Firlik, A. Krupinski- Ptaszek, and R. Lapkiewicz, High-dimensional quan- tum correlation measurements with an adaptively gated hybrid single-photon camera, Optica Quantum 2, 206 (2024)

    2024

  103. [117]

    Courme, C

    B. Courme, C. Verni` ere, P. Svihra, S. Gigan, A. Nomerotski, and H. Defienne, Quantifying high- dimensional spatial entanglement with a single-photon- sensitive time-stamping camera, Opt. Lett. 48, 3439 (2023)

    2023

  104. [118]

    Severini, I

    F. Severini, I. Cusini, F. Madonini, D. Brescia, R. Cam- phausen, A. Cuevas, S. Tisa, and F. Villa, Spatially re- solved event-driven 24 x 24 pixels spad imager with 100 % duty cycle for low optical power quantum entangle- ment detection, IEEE Journal of Solid-State Circuits 5...

    2023

  105. [119]

    Reichert, H

    M. Reichert, H. Defienne, and J. W. Fleischer, Opti- mizing the signal-to-noise ratio of biphoton distribution measurements, Phys. Rev. A 98, 013841 (2018)

    2018

  106. [120]

    Defienne, P

    H. Defienne, P. Cameron, B. Ndagano, A. Lyons, M. Re- ichert, J. Zhao, A. R. Harvey, E. Charbon, J. W. Fleis- cher, and D. Faccio, Pixel super-resolution with spa- tially entangled photons, Nature Communications 13, 3566 (2022)

    2022

  107. [121]

    Rochas, M

    A. Rochas, M. Gosch, A. Serov, P. Besse, R. Popovic, T. Lasser, and R. Rigler, First fully integrated 2-d array of single-photon detectors in standard cmos technology, IEEE Photonics Technology Letters 15, 963 (2003)

    2003

  108. [122]

    Bronzi, F

    D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, 100 000 frames/s 64 × 32 single-photon detector array for 2- d imaging and 3-d ranging, IEEE Journal of Selected Topics in Quantum Electronics 20, 355 (2014)

    2014

  109. [123]

    Lindner, C

    S. Lindner, C. Zhang, I. M. Antolovic, M. Wolf, and E. Charbon, A 252 × 144 spad pixel flash lidar with 1728 dual-clock 48.8 ps tdcs, integrated histogramming and 14.9-to-1 compression in 180nm cmos technology, in 2018 IEEE Symposium on VLSI Circuits (2018) pp. 69–70

    2018

  110. [124]

    R. K. Henderson, N. Johnston, S. W. Hutchings, I. Gy- ongy, T. A. Abbas, N. Dutton, M. Tyler, S. Chan, and J. Leach, 5.7 a 256 ×256 40nm/90nm cmos 3d-stacked 120db dynamic-range reconfigurable time-resolved spad imager, in 2019 IEEE International Solid-State Circuits Conferenc...

    2019

  111. [125]

    Bruschini, H

    C. Bruschini, H. Homulle, I. M. Antolovic, S. Burri, and E. Charbon, Author correction: Single-photon avalanche diode imagers in biophotonics: review and outlook, Light: Science & Applications 9, 12 (2020), an amendment to this paper has been published and can 26 be accessed v...

    2020

  112. [126]

    D.-U. Li, J. Arlt, J. Richardson, R. Walker, A. Buts, D. Stoppa, E. Charbon, and R. Henderson, Real-time fluorescence lifetime imaging system with a 32 × 32 0.13µm cmos low dark-count single-photon avalanche diode array, Opt. Express 18, 10257 (2010)

    2010

  113. [127]

    R. K. Henderson, N. Johnston, H. Chen, D. D.-U. Li, G. Hungerford, R. Hirsch, D. McLoskey, P. Yip, and D. J. Birch, A 192 ×128 time correlated single photon counting imager in 40nm cmos technology, in ESSCIRC 2018 - IEEE 44th European Solid State Circuits Con- ference (ESSCIRC...

    2018

  114. [128]

    Lyons, F

    A. Lyons, F. Tonolini, A. Boccolini, A. Repetti, R. Hen- derson, Y. Wiaux, and D. Faccio, Computational time- of-flight diffuse optical tomography, Nature Photonics 13, 575 (2019)

    2019

  115. [129]

    Gariepy, F

    G. Gariepy, F. Tonolini, R. Henderson, J. Leach, and D. Faccio, Detection and tracking of moving objects hid- den from view, Nature Photonics 10, 23 (2016)

    2016

  116. [130]

    Lubin, R

    G. Lubin, R. Tenne, I. M. Antolovic, E. Charbon, C. Br- uschini, and D. Oron, Quantum correlation measure- ment with single photon avalanche diode arrays, Opt. Express 27, 32863 (2019)

    2019

  117. [131]

    Untern¨ ahrer, B

    M. Untern¨ ahrer, B. Bessire, L. Gasparini, D. Stoppa, and A. Stefanov, Coincidence detection of spatially cor- related photon pairs with a monolithic time-resolving detector array, Opt. Express 24, 28829 (2016)

    2016

  118. [132]

    Bavaresco, N

    J. Bavaresco, N. Herrera Valencia, C. Kl¨ ockl, M. Pivo- luska, P. Erker, N. Friis, M. Malik, and M. Huber, Measurements in two bases are sufficient for certify- ing high-dimensional entanglement, Nature Physics 14, 1032 (2018)

    2018

  119. [133]

    Schneeloch, C

    J. Schneeloch, C. C. Tison, M. L. Fanto, P. M. Als- ing, and G. A. Howland, Quantifying entanglement in a 68-billion-dimensional quantum state space, Nature Communications 10, 2785 (2019)

    2019

  120. [135]

    Bhattacharjee, N

    A. Bhattacharjee, N. Meher, and A. K. Jha, Mea- surement of two-photon position–momentum ein- stein–podolsky–rosen correlations through single- photon intensity measurements, New Journal of Physics 24, 053033 (2022)

    2022

  121. [136]

    A. K. Jha, G. S. Agarwal, and R. W. Boyd, Partial angular coherence and the angular schmidt spectrum of entangled two-photon fields, Phys. Rev. A 84, 063847 (2011)

    2011

  122. [137]

    Kulkarni and A

    G. Kulkarni and A. K. Jha, Single-shot measurement of the orbital-angular-momentum spectrum of light, Na- ture Communications 8, 1054 (2017)

    2017

  123. [138]

    Kulkarni, L

    G. Kulkarni, L. Taneja, S. Aarav, and A. K. Jha, An- gular schmidt spectrum of entangled photons: Deriva- tion of an exact formula and experimental characteriza- tion for noncollinear phase matching, Phys. Rev. A 97, 063846 (2018)

    2018

  124. [139]

    Di Lorenzo Pires, C

    H. Di Lorenzo Pires, C. H. Monken, and M. P. van Ex- ter, Direct measurement of transverse-mode entangle- ment in two-photon states, Phys. Rev. A 80, 022307 (2009)

    2009

  125. [140]

    Hochrainer, M

    A. Hochrainer, M. Lahiri, R. Lapkiewicz, G. B. Lemos, and A. Zeilinger, Quantifying the mo- mentum correlation between two light beams by detecting one, Proceedings of the Na- tional Academy of Sciences 114, 1508 (2017), https://www.pnas.org/doi/pdf/10.1073/pnas.1620979114

    2017 doi

  126. [141]

    Bhattacharjee, S

    A. Bhattacharjee, S. Aarav, and A. K. Jha, Two-shot measurement of spatial coher- ence, Applied Physics Letters 113, 051102 (2018), https://pubs.aip.org/aip/apl/article- pdf/doi/10.1063/1.5041076/13193415/051102 1 online.pdf

    2018 doi

  127. [142]

    P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, Quantum mutual information capacity for high- dimensional entangled states, Phys. Rev. Lett. 108, 143603 (2012)

    2012

  128. [143]

    MANDEL and E

    L. MANDEL and E. WOLF, Coherence properties of optical fields, Rev. Mod. Phys. 37, 231 (1965)

    1965

  129. [144]

    M. V. Fedorov, Y. M. Mikhailova, and P. A. Volkov, Gaussian modelling and schmidt modes of spdc bipho- ton states, Journal of Physics B: Atomic, Molecular and Optical Physics 42, 175503 (2009)

    2009

  130. [145]

    Defienne and S

    H. Defienne and S. Gigan, Spatially entangled photon- pair generation using a partial spatially coherent pump beam, Phys. Rev. A 99, 053831 (2019)

    2019

  131. [146]

    Schneeloch and J

    J. Schneeloch and J. C. Howell, Introduction to the transverse spatial correlations in spontaneous paramet- ric down-conversion through the biphoton birth zone, Journal of Optics 18, 053501 (2016)

    2016

  132. [147]

    Defienne, M

    H. Defienne, M. Reichert, and J. W. Fleischer, Adaptive quantum optics with spatially entangled photon pairs, Phys. Rev. Lett. 121, 233601 (2018)

    2018

  133. [148]

    Defienne, M

    H. Defienne, M. Barbieri, I. A. Walmsley, B. J. Smith, and S. Gigan, Two-photon quantum walk in a mul- timode fiber, Science Advances 2, e1501054 (2016), https://www.science.org/doi/pdf/10.1126/sciadv.1501054

    2016 doi

  134. [149]

    Ferreri, V

    A. Ferreri, V. Ansari, B. Brecht, C. Silberhorn, and P. R. Sharapova, Spatial entanglement and state engi- neering via four-photon hong–ou–mandel interference, Quantum Science and Technology 5, 045020 (2020)

    2020

  135. [150]

    Zhang, F

    Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, Engineering two-photon high-dimensional states through quantum inter- ference, Science Advances 2, e1501165 (2016), https://www.science.org/doi/pdf/10.1126/sciadv.1501165

    2016 doi

  136. [151]

    K. Wang, J. G. Titchener, S. S. Kruk, L. Xu, H.-P. Chung, M. Parry, I. I. Kravchenko, Y.-H. Chen, A. S. Solntsev, Y. S. Kivshar, D. N. Neshev, and A. A. Sukho- rukov, Quantum metasurface for multiphoton interfer- ence and state reconstruction, Science 361, 1104 (2018), https:/...

    2018 doi

  137. [152]

    T. Stav, A. Faerman, E. Maguid, D. Oren, V. Kleiner, E. Hasman, and M. Segev, Quantum entanglement of the spin and orbital angular momentum of pho- tons using metamaterials, Science 361, 1101 (2018), https://www.science.org/doi/pdf/10.1126/science.aat9042

    2018 doi

  138. [153]

    Lib and Y

    O. Lib and Y. Bromberg, Thermal biphotons, APL Pho- tonics 7, 031301 (2022)

    2022

  139. [154]

    Lib and Y

    O. Lib and Y. Bromberg, Spatially entangled airy pho- tons, Opt. Lett. 45, 1399 (2020)

    2020

  140. [155]

    O. Lib, G. Hasson, and Y. Bromberg, Real-time shaping of entangled photons by classical control and feedback, Science Advances 6, eabb6298 (2020), https://www.science.org/doi/pdf/10.1126/sciadv.abb6298

    2020 doi

  141. [156]

    Vaity and L

    P. Vaity and L. Rusch, Perfect vortex beam: Fourier transformation of a bessel beam, Opt. Lett. 40, 597 (2015)

    2015

  142. [157]

    Walborn, C

    S. Walborn, C. Monken, S. P´ adua, and P. Souto Ribeiro, Spatial correlations in parametric down-conversion, 27 Physics Reports 495, 87 (2010)

    2010

  143. [158]

    Gilaberte Basset, F

    M. Gilaberte Basset, F. Setzpfandt, F. Steinlechner, E. Beckert, T. Pertsch, and M. Gr¨ afe, Perspectives for Applications of Quantum Imaging, Laser & Photonics Reviews 13, 10.1002/lpor.201900097 (2019)

    2019 doi

  144. [159]

    Defienne, W

    H. Defienne, W. P. Bowen, M. Chekhova, G. B. Lemos, D. Oron, S. Ramelow, N. Treps, and D. Faccio, Ad- vances in quantum imaging, Nature Photonics 18, 1024 (2024)

    2024

  145. [160]

    Classen, J

    A. Classen, J. von Zanthier, M. O. Scully, and G. S. Agarwal, Superresolution via structured illumination quantum correlation microscopy, Optica 4, 580 (2017)

    2017

  146. [161]

    Untern¨ ahrer, B

    M. Untern¨ ahrer, B. Bessire, L. Gasparini, M. Perenzoni, and A. Stefanov, Super-resolution quantum imaging at the heisenberg limit, Optica 5, 1150 (2018)

    2018

  147. [162]

    Tenne, U

    R. Tenne, U. Rossman, B. Rephael, Y. Israel, A. Krupinski-Ptaszek, R. Lapkiewicz, Y. Silberberg, and D. Oron, Super-resolution enhancement by quan- tum image scanning microscopy, Nature Photonics 13, 116 (2019)

    2019

  148. [163]

    Camphausen, ´A

    R. Camphausen, ´A. Cuevas, L. Duempelmann, R. A. Terborg, E. Wajs, S. Tisa, A. Ruggeri, I. Cusini, F. Steinlechner, and V. Pruneri, A quantum-enhanced wide-field phase imager, Science advances 7, eabj2155 (2021)

    2021

  149. [164]

    Camphausen, A

    R. Camphausen, A. S. Perna, . Cuevas, A. De- muth, J. A. Chill´ on, M. Gr¨ afe, F. Steinlechner, and V. Pruneri, Fast quantum-enhanced imaging with visible-wavelength entangled photons, Optics Express 31, 6039 (2023), publisher: Optica Publishing Group

    2023

  150. [165]

    Brida, M

    G. Brida, M. Genovese, and I. Ruo Berchera, Experi- mental realization of sub-shot-noise quantum imaging, Nat. Photon. 4, 227 (2010)

    2010

  151. [166]

    Samantaray, I

    N. Samantaray, I. Ruo-Berchera, A. Meda, and M. Gen- ovese, Realization of the first sub-shot-noise wide field microscope, Light: Science & Applications 6, e17005 (2017)

    2017

  152. [167]

    Defienne, B

    H. Defienne, B. Ndagano, A. Lyons, and D. Faccio, Po- larization entanglement-enabled quantum holography, Nature Physics 17, 591 (2021)

    2021

  153. [168]

    T¨ opfer, M

    S. T¨ opfer, M. Gilaberte Basset, J. Fuenzalida, F. Stein- lechner, J. P. Torres, and M. Gr¨ afe, Quantum hologra- phy with undetected light, Science advances 8, eabl4301 (2022)

    2022

  154. [169]

    T¨ opfer, S

    S. T¨ opfer, S. Tovar-Perez, J. R. L. Torres, D. Derr, E. Giese, J. Fuenzalida, and M. Gr¨ afe, Synthetic quan- tum holography with undetected light, Optica Quantum 3, 129 (2025), publisher: Optica Publishing Group

    2025

  155. [170]

    G. B. Lemos, V. Borish, G. D. Cole, S. Ramelow, R. Lapkiewicz, and A. Zeilinger, Quantum imaging with undetected photons, Nature 512, 409 (2014)

    2014

  156. [171]

    Fuenzalida, E

    J. Fuenzalida, E. Giese, and M. Gr¨ afe, Nonlinear inter- ferometry: A new approach for imaging and sensing, Advanced Quantum Technologies 7, 2300353 (2024)

    2024

  157. [172]

    Gilaberte Basset, A

    M. Gilaberte Basset, A. Hochrainer, S. T¨ opfer, F. Riexinger, P. Bickert, J. Le´ on-Torres, F. Stein- lechner, and M. Gr¨ afe, Video-Rate Imaging with Un- detected Photons, Laser & Photonics Reviews 15, 10.1002/lpor.202000327 (2021)

    2021 doi

  158. [173]

    Lloyd, Enhanced sensitivity of photodetection via quantum illumination, Science 321, 1463 (2008)

    S. Lloyd, Enhanced sensitivity of photodetection via quantum illumination, Science 321, 1463 (2008)

    2008

  159. [174]

    Gregory, P.-A

    T. Gregory, P.-A. Moreau, E. Toninelli, and M. J. Pad- gett, Imaging through noise with quantum illumination, Science advances 6, eaay2652 (2020)

    2020

  160. [175]

    Fuenzalida, M

    J. Fuenzalida, M. Gilaberte Basset, S. T¨ opfer, J. P. Torres, and M. Gr¨ afe, Experimental quantum imaging distillation with undetected light, Science advances 9, eadg9573 (2023)

    2023

  161. [176]

    E. A. Ortega, K. Dovzhik, J. Fuenzalida, S. Wengerowsky, J. C. Alvarado-Zacarias, R. F. Shiozaki, R. Amezcua-Correa, M. Bohmann, and R. Ursin, Experimental space-division multiplexed polarization-entanglement distribution through 12 paths of a multicore fiber, PRX quantum 2, 0...

    2021

  162. [177]

    Achatz, L

    L. Achatz, L. Bulla, S. Ecker, E. A. Ortega, M. Bar- tokos, J. C. Alvarado-Zacarias, R. Amezcua-Correa, M. Bohmann, R. Ursin, and M. Huber, Simultaneous transmission of hyper-entanglement in three degrees of freedom through a multicore fiber, npj Quantum Infor- mation 9, 45 (2023)

    2023

  163. [178]

    Ecker, J

    S. Ecker, J. Pseiner, J. Piris, and M. Bohmann, Ad- vances in entanglement-based QKD for space applica- tions, in International Conference on Space Optics — ICSO 2022 , Vol. 12777 (SPIE, 2023) pp. 925–945

    2022

  164. [179]

    S.-H. Wei, B. Jing, X.-Y. Zhang, J.-Y. Liao, C.-Z. Yuan, B.-Y. Fan, C. Lyu, D.-L. Zhou, Y. Wang, G.-W. Deng, H.-Z. Song, D. Oblak, G.-C. Guo, and Q. Zhou, Towards Real-World Quantum Networks: A Review, Laser & Photonics Reviews 16, 2100219 (2022), eprint: https://onlinelibrary...

    2022 doi

  165. [180]

    E. A. Ortega, J. Fuenzalida, K. Dovzhik, R. F. Shiozaki, J. Carlos Alvarado-Zacarias, R. Amezcua-Correa, M. Bohmann, S. Wengerowsky, and R. Ursin, Imple- mentation of space-division multiplexed entanglement- based quantum cryptography over multicore fiber, Op- tica Quantum 2, ...

    2024

  166. [181]

    Defienne, M

    H. Defienne, M. Barbieri, I. A. Walmsley, B. J. Smith, and S. Gigan, Two-photon quantum walk in a multi- mode fiber, Science advances 2, e1501054 (2016)

    2016

  167. [182]

    N. H. Valencia, S. Goel, W. McCutcheon, H. Defienne, and M. Malik, Unscrambling entanglement through a complex medium, Nature Physics 16, 1112 (2020)

    2020

  168. [183]

    Gr¨ afe, R

    M. Gr¨ afe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, Integrated photonic quantum walks, Journal of Optics 18, 103002 (2016), publisher: IOP Publishing

    2016

  169. [184]

    Di Giuseppe, L

    G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, Einstein- Podolsky-Rosen Spatial Entanglement in Ordered and Anderson Photonic Lattices, Physical Review Letters 110, 150503 (2013)...

    2013

  170. [185]

    Gr¨ afe, R

    M. Gr¨ afe, R. Heilmann, R. Keil, T. Eichelkraut, M. Heinrich, S. Nolte, and A. Szameit, Correlations of indistinguishable particles in non-Hermitian lattices, New Journal of Physics 15, 033008 (2013), publisher: IOP Publishing

    2013

  171. [186]

    Cameron, B

    P. Cameron, B. Courme, C. Verni` ere, R. Pandya, D. Faccio, and H. Defienne, Adaptive optical imaging with entangled photons, Science 383, 1142 (2024)

    2024

  172. [187]

    D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, Observation of Two-Photon “Ghost” In- terference and Diffraction, Physical Review Letters 74, 3600 (1995). 28

    1995

  173. [188]

    T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Optical imaging by means of two-photon quantum entanglement, Physical Review A 52, R3429 (1995)

    1995

  174. [189]

    R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Pad- gett, EPR-based ghost imaging using a single-photon- sensitive camera, New Journal of Physics 15, 073032 (2013)

    2013

  175. [190]

    Fickler, M

    R. Fickler, M. Krenn, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, Real-Time Imaging of Quantum Entan- glement, Scientific Reports 3, 1914 (2013), publisher: Nature Publishing Group

    2013

  176. [191]

    P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, Imaging with a small number of pho- tons, Nature Communications 6, 5913 (2015), publisher: Nature Publishing Group

    2015

  177. [192]

    C. C. Kim and G. Kanner, Infrared two-color ghost imaging using entangled beams, in Quantum Commu- nications and Quantum Imaging VIII , Vol. 7815 (SPIE,

  178. [193]

    M. H. Rubin and Y. Shih, Resolution of ghost imag- ing for nondegenerate spontaneous parametric down- conversion, Physical Review A 78, 033836 (2008)

    2008

  179. [194]

    Karmakar and Y

    S. Karmakar and Y. Shih, Two-color ghost imaging with enhanced angular resolving power, Physical Review A 81, 033845 (2010), publisher: American Physical Soci- ety

    2010

  180. [195]

    R. S. Aspden, N. R. Gemmell, P. A. Morris, D. S. Tasca, L. Mertens, M. G. Tanner, R. A. Kirkwood, A. Rug- geri, A. Tosi, R. W. Boyd, G. S. Buller, R. H. Hadfield, and M. J. Padgett, Photon-sparse microscopy: visible light imaging using infrared illumination, Optica2, 1049 (2015)

    2015

  181. [196]

    Two- Photon

    R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two- Photon” Coincidence Imaging with a Classical Source, Physical Review Letters 89, 113601 (2002), publisher: American Physical Society

    2002

  182. [197]

    Valencia, G

    A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Two-Photon Imaging with Thermal Light, Physical Re- view Letters 94, 063601 (2005)

    2005

  183. [198]

    J. H. Shapiro, Computational ghost imaging, Physical Review A 78, 061802 (2008)

    2008

  184. [199]

    Bromberg, O

    Y. Bromberg, O. Katz, and Y. Silberberg, Ghost imag- ing with a single detector, Physical Review A79, 053840 (2009), publisher: American Physical Society

    2009

  185. [200]

    Moodley and A

    C. Moodley and A. Forbes, All-digital quantum ghost imaging: tutorial, JOSA B 40, 3073 (2023), publisher: Optica Publishing Group

    2023

  186. [201]

    Moreau, E

    P.-A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, Ghost Imaging Using Optical Correlations, Laser & Photonics Reviews 12, 1700143 (2018), eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/lpor.201700143

    2018 doi

  187. [202]

    E. J. Candes and M. B. Wakin, An Introduction To Compressive Sampling, IEEE Signal Processing Maga- zine 25, 21 (2008), conference Name: IEEE Signal Pro- cessing Magazine

    2008

  188. [203]

    Romberg, Imaging via Compressive Sampling, IEEE Signal Processing Magazine 25, 14 (2008), conference Name: IEEE Signal Processing Magazine

    J. Romberg, Imaging via Compressive Sampling, IEEE Signal Processing Magazine 25, 14 (2008), conference Name: IEEE Signal Processing Magazine

    2008

  189. [204]

    O. Katz, Y. Bromberg, and Y. Silberberg, Compres- sive ghost imaging, Applied Physics Letters 95, 131110 (2009)

    2009

  190. [205]

    Gregory, P.-A

    T. Gregory, P.-A. Moreau, E. Toninelli, and M. J. Padgett, Imaging through noise with quantum illu- mination, Science Advances 6, eaay2652 (2020), eprint: https://www.science.org/doi/pdf/10.1126/sciadv.aay2652

    2020 doi

  191. [206]

    Reichert, H

    M. Reichert, H. Defienne, and J. W. Fleischer, Massively Parallel Coincidence Counting of High-Dimensional En- tangled States, Scientific Reports 8, 7925 (2018), pub- lisher: Nature Publishing Group

    2018

  192. [207]

    Toninelli, P.-A

    E. Toninelli, P.-A. Moreau, T. Gregory, A. Mihalyi, M. Edgar, N. Radwell, and M. Padgett, Resolution- enhanced quantum imaging by centroid estimation of biphotons, Optica 6, 347 (2019), publisher: Optica Pub- lishing Group

    2019

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