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REVIEW 5 minor 58 references

Single-acquisition tomography of photonic qubits with structured media

T0 review · 0 major / 5 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read Three fixed liquid-crystal metasurfaces map any photonic polarization qubit into a single-shot diffraction pattern that fully reconstructs the state.

desk verdict Fixed three-plate LC metasurface gadget that does single-acquisition polarization tomography for any photon number via post-selected coincidences; data look solid against Stokes benchmarks. read the letter →

arxiv 2607.03052 v1 pith:DU35EIMW submitted 2026-07-03 quant-ph physics.optics

Francesco Di Colandrea , Yingwen Zhang , John Grace , Dilip Paneru , Alessio D'Errico , Ebrahim Karimi This is my paper
classification quant-phphysics.optics
keywords quantumstatetomographyphotonicqubitsliquid-crystalmetasurfacesspin-orbitinteractionSIC-POVMMUBsingle-acquisitionmeasurementpolarization
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

Standard polarization tomography needs many sequential projections and apparatus reconfigurations; the number of settings grows rapidly with photon number. This paper shows that three stacked liquid-crystal metasurfaces with carefully designed optic-axis patterns can implement a unitary that couples polarization to discrete transverse-momentum modes so that a single far-field image (or set of coincidence images) already encodes an informationally complete set of projections. The same fixed device works for any photon number: single photons are read out with a camera, multi-photon states by post-selecting n-fold coincidences. Experiments reconstruct both pure and mixed single-qubit states and a two-photon mixed state with fidelities comparable to conventional multi-setting Stokes tomography, establishing a compact, reconfigurable-free route to photonic state characterization.

What carries the argument

The space-periodic unitary U(x) realized by three liquid-crystal plates (retarder settings π/2, π, π/2). Its Fourier components V_n are engineered so that the projectors E_n = V_n† |Π angle⟨Π| V_n exactly match a target tomographic POVM on the designed orders; unitarity is restored by numerical optimization of the remaining Fourier coefficients.

What would settle it

Prepare a known pure state (for example |L angle), record the single-shot diffraction pattern through the fabricated device, reconstruct the density matrix from the designed orders, and check whether the fidelity with the independently measured Stokes matrix falls below ~90 % or the Bhattacharyya coefficient with the ideal probability distribution drops well below the reported ~92 %.

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Extended reading notes

Core claim

A fixed three-metasurface unitary maps an unknown polarization state into a set of diffraction orders whose intensities equal (up to a known scale) the outcome probabilities of a chosen informationally complete POVM (MUB or SIC-POVM). Because the mapping is photon-number independent, the same optical gadget yields full tomography of single- and multi-photon polarization states from one acquisition, with photon number selected only in post-processing.

Load-bearing premise

Free-space propagation between the three closely stacked plates can be neglected and fabrication/alignment errors leave the actual diffraction projectors close enough to the design POVM for the reconstruction to stay informationally complete.

Editorial extensions

If this is right

  • Full polarization tomography of multi-photon states becomes a single-camera (or single coincidence-camera) measurement with no wave-plate reconfiguration.
  • The same three-plate stack can be reused for any photon number; only the post-selection of coincidence order changes.
  • Left/right and orthogonal-polarization symmetries automatically supply up to four independent reconstructions that can be averaged to suppress experimental imperfections.
  • The design procedure is not limited to MUBs or SIC-POVMs; any informationally complete set of projectors can be targeted by re-optimizing the optic-axis patterns.

Reading between the lines

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

  • Because the mapping is linear and unitary, the same hardware could in principle perform single-shot process tomography or shadow-style estimation of entanglement witnesses without full state reconstruction.
  • Extending the optic-axis patterning into two dimensions would allow simultaneous tomography of polarization and a second spatial degree of freedom (orbital angular momentum) on one chip.
  • Efficiency losses into unused diffraction orders set a practical limit on large photon numbers; anti-reflection coatings and tighter optimization of extraneous modes would directly raise that ceiling.
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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

0 major / 5 minor

Summary. The manuscript introduces a fixed three-liquid-crystal-metasurface platform that implements a periodic, space-dependent SU(2) unitary. Target MUB or SIC-POVM projectors are mapped analytically onto a subset of diffraction-order operators V_n (Eqs. 4–5, 11); residual Fourier coefficients are fixed by numerical minimization of a unitarity cost (Eq. 12). In the far field a single polarization projection yields an informationally complete set of intensities, so the input polarization density matrix is reconstructed without reconfiguring the apparatus. The same three-plate device is photon-number agnostic: multi-photon states are recovered by post-selecting n-fold coincidences among vertically displaced diffraction patterns. Experiments report single-photon fidelities of 94–99 % versus independent Stokes polarimetry (Bhattacharyya coefficients ~92 %) and a two-photon average fidelity of 94.2 % for a mixed state of purity ~0.53.

Significance. If the results hold, the work supplies a compact, reconfigurable-free route to full polarization tomography that scales to arbitrary photon number by post-selection alone. The analytic Fourier matching plus residual unitarity optimization is clean and free of fitted reconstruction parameters; the experimental fidelities against independent Stokes tomography and the explicit two-photon demonstration constitute concrete, falsifiable evidence. The platform therefore offers a practical advance for multi-photon characterization and for any setting in which sequential wave-plate reconfiguration is undesirable.

minor comments (5)
  1. Sec. II.C and Fig. 1: free-space propagation between the three plates is stated to be negligible once they are “closely stacked,” yet no quantitative bound (optical path difference relative to Rayleigh range or coherence length) is given. A short estimate would strengthen the claim.
  2. Figs. 2–3: the experimental diffraction patterns show residual intensity in nominally dark orders (e.g., n=1 for |R angle input in the SIC case). A brief discussion of the dominant fabrication/alignment error sources would help readers assess residual POVM fidelity.
  3. Eq. (2) and the reconstruction paragraphs: the precise inversion algorithm (linear inversion, maximum-likelihood, etc.) is not stated. Adding one sentence would improve reproducibility.
  4. Two-photon section: the residual coherence parameter γ that appears in the supplementary mixed-state model is never quoted for the measured data; reporting its value would clarify how close the prepared state is to the ideal mixture.
  5. Typographical: “THEOR Y” and “RESUL TS” headings contain stray spaces; “n-fold” is inconsistently italicized.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: target POVMs are imposed by design, unitarity is optimized residual, and reconstructions are validated against independent Stokes tomography.

  1. self citation load bearing [Sec. II.C, paragraph on optical implementation]
    "It has been demonstrated that a minimal sequence of three liquid-crystal metasurfaces, W1-W2-W3, tuned so that δ1=δ3=π/2 and δ2=π, can always be found to implement an arbitrary space-dependent polarization transformation [43, 44]."

    The constructive claim that three plates suffice for any U(x) rests solely on prior papers by overlapping authors. The citation is not load-bearing for the tomography completeness or experimental fidelities, which stand independently; it is only a fabrication convenience. Hence only a minor (score-1) flag.

full rationale

The derivation is constructive engineering, not a closed prediction loop. Target informationally complete sets (MUB or SIC-POVM) are chosen a priori; Fourier coefficients of U(x) for the designed diffraction orders are fixed analytically by En = λ^{2} E_target_n (Eqs. 5, 11); remaining coefficients are variationally adjusted only to restore unitarity via the cost L (Eq. 12). Completeness of the multi-photon joint POVM then follows by the standard tensor-product argument (Eq. 6). Experimental density matrices are obtained by ordinary inversion of measured intensities and are compared to fully independent sequential Stokes polarimetry (fidelities 94–99 % single-photon, 94 % two-photon). Self-citations ([43,44]) supply only the known three-plate decomposition that realizes an arbitrary space-dependent SU(2) map; they do not underwrite uniqueness of the tomography result itself. No parameter is fitted to data and then re-presented as a prediction, and no self-definitional identity is disguised as a derivation. Score 1 reflects only the minor, non-load-bearing self-citation of the implementation toolkit.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The result rests on standard quantum measurement theory, the known ability of three liquid-crystal plates to realize arbitrary space-dependent SU(2) transformations, and a numerical optimization that enforces unitarity after analytic Fourier matching. No new physical entities are postulated; free parameters are the usual design choices (period, discretization, number of Fourier modes, efficiency threshold) that any metasurface designer must set.

free parameters (3)
  • N (max Fourier harmonics) and next (extraneous modes) = N=11 (MUB), efficiency ~77–78 %
    Chosen variationally until theoretical efficiency exceeds ~77 %; different values for MUB (N=11) and SIC-POVM.
  • spatial period Λ and discretization Δx = Λ=2.5 mm, Δx=4 µm
    Set by fabrication convenience and beam-waist matching; enter the Fourier transform that defines Vn.
  • retardation voltages setting δ1=δ3=π/2, δ2=π
    Electrically tuned after fabrication; small deviations alter the realized unitary.
assumptions (4)
  • standard math A periodic space-dependent SU(2) unitary can be expanded in discrete transverse-momentum modes whose intensities realize a chosen POVM after a global polarization projection.
    Eqs. (1)–(5); standard Fourier analysis of periodic Jones matrices.
  • domain assumption Three liquid-crystal metasurfaces with retardations π/2, π, π/2 can implement any prescribed space-dependent polarization transformation U(x).
    Cited from Refs. [43,44] and used in Sec. II.C to convert the optimized U(x) into optic-axis patterns θi(x).
  • standard math If {En} is informationally complete on one qubit, the tensor-product set is informationally complete on m qubits.
    Stated after Eq. (6) and referenced to [41]; used to claim multi-photon completeness without redesign.
  • domain assumption Free-space propagation between the three stacked plates is negligible.
    Explicit experimental requirement in Sec. III; if violated the composite unitary is no longer the designed U(x).

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Cite this review

Pith. "Pith review of Single-acquisition tomography of photonic qubits with structured media." pith.science (2026). https://pith.science/paper/DU35EIMW

@misc{pith2026260703052,
  author       = {Pith},
  title        = {Pith review of: Single-acquisition tomography of photonic qubits with structured media},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DU35EIMW}},
  note         = {Machine review of arXiv:2607.03052}
}
abstract

Quantum state tomography is an essential tool for characterizing quantum systems and underpins nearly every experimental realization of quantum technologies. Conventional tomography relies on performing a sequence of projective measurements on many identical copies of a quantum state, requiring the measurement apparatus to be reconfigured between successive acquisitions. As the Hilbert-space dimension increases, the number of required measurements grows rapidly; in practice, additional overcomplete measurements are often performed to improve robustness to experimental imperfections. Here, we introduce a tomography platform based on structured anisotropic media that performs informationally complete measurements of photonic polarization qubits within a single acquisition. The approach employs three liquid-crystal metasurfaces with spatially varying optic-axis orientations that transform the input polarization into a far-field distribution of discrete transverse-momentum modes. Each diffraction pattern uniquely determines the polarization state, enabling its reconstruction without sequential changes to the measurement apparatus. Unlike previous implementations, our scheme is intrinsically photon-number independent: the same optical device operates identically for arbitrary photon numbers, while the desired photon-number sector can be selected afterwards through post-selection of the corresponding $n$-fold coincidence events. We experimentally demonstrate single-frame quantum state tomography of both single- and two-photon polarization states, providing a simple and scalable route toward efficient quantum-state characterization.

Figures

Figures reproduced from arXiv: 2607.03052 by the authors.

Figure 1
Figure 1. Single-acquisition tomography with liquid-crystal metasurfaces. (a) Patterns of two liquid-crystal meta￾surfaces for MUB and SIC-POVM tomography (left and right, respectively), viewed between crossed polarizers. Scale bars indicate the device dimensions. (b) An unknown polarization state, ρ, either pure or mixed, is coupled to transverse momentum through a space-dependent polarization transformation U, implemented w… view at source ↗
Figure 2
Figure 2. MUB tomography with liquid-crystal metasurfaces. (a) Liquid-crystal patterns for the implementation of single-acquisition tomography with MUB states. (b) From the output diffraction pattern, an experimental probability distribution P(n) is extracted. The probability of designed modes is proportional to the outcome of a set of tomographic measurements. In the example, an input state |L⟩ was considered. (c) The symmet… view at source ↗
Figure 3
Figure 3. SIC-POVM tomography with liquid-crystal metasurfaces. (a) Liquid-crystal patterns for the implementation of single-acquisition tomography with SIC-POVM states. (b) From the output diffraction pattern, an experimental probability distribution P(n) is extracted. In the example, an input state |R⟩ was considered. (c) The symmetry of the pattern can be used to extract two independent “left” (ρL) and “right” (ρR) tomogra… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Two-photon quantum state tomography. The set of metasurfaces implementing single-acquisition SIC-POVM tomography is employed with two-photon input states. A time-stamping camera, placed in the far field, enables detection of space-resolved coincidence events. Upon a si…

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Works this paper leans on

58 extracted references

  1. [1]

    James, D. F. V., Kwiat, P. G., Munro, W. J. and White, A. G.,Measurement of qubits, Physical Review A64, 052312 (2001)

    2001

  2. [2]

    and Kwiat, P.,Photonic State Tomography, Advances In Atomic, Molecular, and Opti- cal Physics52, 105 (2005)

    Altepeter, J., Jeffrey, E. and Kwiat, P.,Photonic State Tomography, Advances In Atomic, Molecular, and Opti- cal Physics52, 105 (2005)

    2005

  3. [3]

    S., Goldstein, D

    Tyo, J. S., Goldstein, D. L., Chenault, D. B. and Shaw, J. A.,Review of passive imaging polarimetry for remote sensing applications, Applied Optics45, 5453 (2006)

    2006

  4. [4]

    and Gruev, V.,Bio-inspired color-polarization imager for real-time in situ imaging, Optica4, 1263 (2017)

    Garcia, M., Edmiston, C., Marinov, R., Vail, A. and Gruev, V.,Bio-inspired color-polarization imager for real-time in situ imaging, Optica4, 1263 (2017)

    2017

  5. [5]

    and Booth, M

    He, C., He, H., Chang, J., Chen, B., Ma, H. and Booth, M. J.,Polarisation optics for biomedical and clinical ap- plications: a review, Light: Science & Applications10, 194 (2021)

    2021

  6. [6]

    M., Blume-Kohout, R., Scott, A

    Renes, J. M., Blume-Kohout, R., Scott, A. J. and Caves, C. M.,Symmetric informationally complete quan- tum measurements, Journal of Mathematical Physics45, 2171 (2004)

    2004

  7. [7]

    A., Sych, D., Leuchs, G., S´ anchez-Soto, L

    Bent, N., Qassim, H., Tahir, A. A., Sych, D., Leuchs, G., S´ anchez-Soto, L. L., Karimi, E. and Boyd, R. W.,Exper- imental Realization of Quantum Tomography of Photonic Qudits via Symmetric Informationally Complete Positive Operator-Valued Measures, Physical Review X5, 041006 (2015)

    2015

  8. [8]

    and Wehner, S.,Bell nonlocality, Reviews of modern physics 86, 419 (2014)

    Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. and Wehner, S.,Bell nonlocality, Reviews of modern physics 86, 419 (2014)

    2014

Show all 58 references
  1. [9]

    and Pau, S.,Full-Stokes imaging polarimeter using an array of elliptical polarizer, Optics Express22, 3063 (2014)

    Hsu, W.-L., Myhre, G., Balakrishnan, K., Brock, N., Ibn- Elhaj, M. and Pau, S.,Full-Stokes imaging polarimeter using an array of elliptical polarizer, Optics Express22, 3063 (2014)

    2014

  2. [10]

    Pors, A., Nielsen, M. G. and Bozhevolnyi, S. I.,Plas- monic metagratings for simultaneous determination of Stokes parameters, Optica2, 716 (2015)

    2015

  3. [11]

    Wen, D.et al.,Metasurface for characterization of the po- larization state of light, Optics Express23, 10272 (2015)

    2015

  4. [12]

    T., T¨ or¨ ok, P., Foreman, M

    Chen, W. T., T¨ or¨ ok, P., Foreman, M. R., Liao, C. Y., Tsai, W.-Y., Wu, P. R. and Tsai, D. P.,Integrated plas- monic metasurfaces for spectropolarimetry, Nanotechnol- ogy27, 224002 (2016)

    2016

  5. [13]

    and Zhao, M.,Design of ultracompact polarimeters based on dielectric metasurfaces, Optics Let- ters42, 1580 (2017)

    Wei, S., Yang, Z. and Zhao, M.,Design of ultracompact polarimeters based on dielectric metasurfaces, Optics Let- ters42, 1580 (2017)

    2017

  6. [14]

    M., Arbabi, A

    Arbabi, E., Kamali, S. M., Arbabi, A. and Faraon, A., Full-Stokes Imaging Polarimetry Using Dielectric Meta- surfaces, ACS Photonics5, 3132 (2018)

    2018

  7. [15]

    and Wang, M.,Im- plement quantum tomography of polarization-entangled states via nondiffractive metasurfaces, Applied Physics Letters121, 081703 (2022)

    Wang, Z., Jiang, Y., Gao, Y.-J., Fan, R.-H., Qi, D.-X., Zhong, R., Zhang, H.-L., Peng, R.-W. and Wang, M.,Im- plement quantum tomography of polarization-entangled states via nondiffractive metasurfaces, Applied Physics Letters121, 081703 (2022)

    2022

  8. [16]

    and Tanemura, T.,Compact and scalable po- larimetric self-coherent receiver using a dielectric meta- 9 surface, Optica10, 604 (2023)

    Soma, G., Nomoto, Y., Umezawa, T., Yoshida, Y., Nakano, Y. and Tanemura, T.,Compact and scalable po- larimetric self-coherent receiver using a dielectric meta- 9 surface, Optica10, 604 (2023)

    2023

  9. [17]

    Fan, Q.et al.,Disordered metasurface enabled single-shot full-Stokes polarization imaging leveraging weak dichro- ism, Nature Communications14, 7180 (2023)

    2023

  10. [18]

    and Lu, H.,Efficient characterizations of multiphoton states with an ultra-thin optical device, Nature Communications15, 3944 (2024)

    An, K., Liu, Z., Zhang, T., Li, S., Zhou, Y., Yuan, X., Wang, L., Zhang, W., Wang, G. and Lu, H.,Efficient characterizations of multiphoton states with an ultra-thin optical device, Nature Communications15, 3944 (2024)

    2024

  11. [19]

    E.,Polarization imaging, Applied Optics20, 1537 (1981)

    Solomon, J. E.,Polarization imaging, Applied Optics20, 1537 (1981)

    1981

  12. [20]

    Azzam, R. M. A.,Stokes-vector and Mueller-matrix po- larimetry (Invited), Journal of the Optical Society of America33, 1396 (2016)

    2016

  13. [21]

    Y., Rodr´ ıguez-Fortu˜ no, F

    Bliokh, K. Y., Rodr´ ıguez-Fortu˜ no, F. J., Nori, F. and Zayats, A. V.,Spin–orbit interactions of light, Nature Photonics9, 796 (2015)

    2015

  14. [22]

    and Marrucci, L.,Spin–orbit photonics, Na- ture Photonics9, 776 (2015)

    Cardano, F. and Marrucci, L.,Spin–orbit photonics, Na- ture Photonics9, 776 (2015)

    2015

  15. [23]

    Mueller, J. P. B., Leosson, K. and Capasso, F.,Ultracom- pact metasurface in-line polarimeter, Optica3, 42 (2016)

    2016

  16. [24]

    J., Griol, A

    Espinosa-Soria, A., Rodr´ ıguez-Fortu˜ no, F. J., Griol, A. and Mart´ ınez, A.,On-Chip Optimal Stokes Nanopo- larimetry Based on Spin–Orbit Interaction of Light, Nano Letters17, 3139 (2017)

    2017

  17. [25]

    Yang, Z.et al.,Generalized Hartmann-Shack array of di- electric metalens sub-arrays for polarimetric beam profil- ing, Nature Communications9, 4607 (2018)

    2018

  18. [26]

    and Yuan, X.,Multifunctional geometric phase optical element for high-efficiency full Stokes imaging po- larimetry, Photonics Research7, 1066 (2019)

    Dai, Y., Zhang, Y., Xie, Y., Wang, D., Wang, X., Lei, T., Min, C. and Yuan, X.,Multifunctional geometric phase optical element for high-efficiency full Stokes imaging po- larimetry, Photonics Research7, 1066 (2019)

    2019

  19. [27]

    Wang, K.et al.,Quantum metasurface for multiphoton interference and state reconstruction, Science361, 1104 (2018)

    2018

  20. [28]

    Lung, S., Wang, K., Pedersen, N. R. H., Setzpfandt, F. and Sukhorukov, A. A.,Robust Classical and Quantum Polarimetry with a Single Nanostructured Metagrating, ACS Photonics11, 1060 (2024)

    2024

  21. [29]

    A., D’Aversa, G., Chevalier, P., Shi, Z., Chen, W

    Rubin, N. A., D’Aversa, G., Chevalier, P., Shi, Z., Chen, W. T. and Capasso, F.,Matrix Fourier optics enables a compact full-Stokes polarization camera, Science365, eaax1839 (2019)

    2019

  22. [30]

    and Arteaga, O.,Mueller matrix imaging with a polarization camera: application to microscopy, Optics Express29, 34723 (2021)

    Gottlieb, D. and Arteaga, O.,Mueller matrix imaging with a polarization camera: application to microscopy, Optics Express29, 34723 (2021)

    2021

  23. [31]

    and Li, X.,Meta-grating- lens–based monolithic polarization camera, Science Ad- vances11, eadx9886 (2025)

    Li, F.-J., Feng, Z., Wan, Z., Shi, T., Qiu, S., Zeng, J.-H., Song, S., Wang, S., Deng, Z.-L. and Li, X.,Meta-grating- lens–based monolithic polarization camera, Science Ad- vances11, eadx9886 (2025)

    2025

  24. [32]

    and Arteaga, O.,A simple pathway for complete polarization vision, Scientific Reports15, 8885 (2025)

    Bian, S. and Arteaga, O.,A simple pathway for complete polarization vision, Scientific Reports15, 8885 (2025)

    2025

  25. [33]

    and Palma, G

    Innocenti, L., Lorenzo, S., Palmisano, I., Ferraro, A., Paternostro, M. and Palma, G. M.,Potential and limita- tions of quantum extreme learning machines, Communi- cations Physics6, 118 (2023)

    2023

  26. [34]

    and Conti, C.,Single-shot polarimetry of vector beams by supervised learning, Nature Communica- tions14, 1831 (2023)

    Pierangeli, D. and Conti, C.,Single-shot polarimetry of vector beams by supervised learning, Nature Communica- tions14, 1831 (2023)

    2023

  27. [35]

    and Pierangeli, D.,Single-Shot Full-Stokes Analysis of Partially-Polarized Light With a Photonic Deep Random Neural Network, Laser & Pho- tonics Reviews , e01467 (2025)

    Petrini, A., Conti, C. and Pierangeli, D.,Single-Shot Full-Stokes Analysis of Partially-Polarized Light With a Photonic Deep Random Neural Network, Laser & Pho- tonics Reviews , e01467 (2025)

    2025

  28. [36]

    Suprano, A.et al.,Experimental Property Reconstruc- tion in a Photonic Quantum Extreme Learning Machine, Physical Review Letters132, 160802 (2024)

    2024

  29. [37]

    Zia, D.et al.,Quantum reservoir computing for photonic entanglement witnessing, Science Advances11, eady7987 (2025)

    2025

  30. [38]

    Nomerotski, A., Chekhlov, M., Dolzhenko, D., Glazen- borg, R., Farella, B., Keach, M., Mahon, R., Orlov, D. and Svihra, P.,Intensified Tpx3Cam, a fast data-driven optical camera with nanosecond timing resolution for sin- gle photon detection in quantum applications, Journal of...

    2023

  31. [39]

    and Marrucci, L.,Two-dimensional topo- logical quantum walks in the momentum space of struc- tured light, Optica7, 108 (2020)

    D’Errico, A., Cardano, F., Maffei, M., Dauphin, A., Bar- boza, R., Esposito, C., Piccirillo, B., Lewenstein, M., Massignan, P. and Marrucci, L.,Two-dimensional topo- logical quantum walks in the momentum space of struc- tured light, Optica7, 108 (2020)

    2020

  32. [40]

    W.,Introduction to Fourier optics(Roberts and Company publishers, 2005)

    Goodman, J. W.,Introduction to Fourier optics(Roberts and Company publishers, 2005)

    2005

  33. [41]

    Wiersema, R., Guerini, L., Carrasquilla, J. F. and Aolita, L.,Circuit connectivity boosts by quantum-classical- quantum interfaces, Physical Review Research4, 043221 (2022)

    2022

  34. [42]

    and Santamato, E.,Photon spin-to-orbital angular mo- mentum conversion via an electrically tunable q-plate, Applied Physics Letters97, 241104 (2010)

    Piccirillo, B., D’Ambrosio, V., Slussarenko, S., Marrucci, L. and Santamato, E.,Photon spin-to-orbital angular mo- mentum conversion via an electrically tunable q-plate, Applied Physics Letters97, 241104 (2010)

    2010

  35. [43]

    and Cardano, F.,Ultra-long quan- tum walks via spin–orbit photonics, Optica10, 324 (2023)

    Di Colandrea, F., Babazadeh, A., Dauphin, A., Massig- nan, P., Marrucci, L. and Cardano, F.,Ultra-long quan- tum walks via spin–orbit photonics, Optica10, 324 (2023)

    2023

  36. [44]

    G., Di Colandrea, F., Marrucci, L

    Ammendola, M. G., Di Colandrea, F., Marrucci, L. and Cardano, F.,Large-scale free-space photonic circuits in two dimensions, Advanced Photonics7, 016006 (2025)

    2025

  37. [45]

    and Marrucci, L., Q-plate technology: a progress review (Invited), Journal of the Optical Society of America B36, D70 (2019)

    Rubano, A., Cardano, F., Piccirillo, B. and Marrucci, L., Q-plate technology: a progress review (Invited), Journal of the Optical Society of America B36, D70 (2019)

    2019

  38. [46]

    Nielsen, M. A. and Chuang, I. L.,Quantum computation and quantum information(Cambridge university press, 2010)

    2010

  39. [47]

    and Liscidini, M.,A tailor-made quantum state tomogra- phy approach, APL Quantum1, 036112 (2024)

    Binosi, D., Garberoglio, G., Maragnano, D., Dapor, M. and Liscidini, M.,A tailor-made quantum state tomogra- phy approach, APL Quantum1, 036112 (2024)

    2024

  40. [48]

    Zambrano, L., Farina, D., Pagliaro, E., Taddei, M. M. and Acin, A.,Certification of quantum state functions under partial information, Quantum8, 1442 (2024)

    2024

  41. [49]

    Aaronson, S.,Shadow Tomography of Quantum States, SIAM Journal on Computing49, STOC18 (2020)

    2020

  42. [50]

    Wang, M.et al.,Characterization of Orbital Angular Mo- mentum Quantum States Empowered by Metasurfaces, Nano Letters23, 3921 (2023)

    2023

  43. [51]

    and Wang, K.,Can Randomly Structured Meta- surfaces Be Used for Quantum Tomography of High- Dimensional Spatial Qudits?, ACS Photonics12, 6797 (2025)

    Niu, Y. and Wang, K.,Can Randomly Structured Meta- surfaces Be Used for Quantum Tomography of High- Dimensional Spatial Qudits?, ACS Photonics12, 6797 (2025)

    2025

  44. [52]

    and Segev, M.,Any DOF all at once: single photon state tomography in a single measurement setup, Optics Express34, 18997 (2026)

    Shafran, R., Ziv, R. and Segev, M.,Any DOF all at once: single photon state tomography in a single measurement setup, Optics Express34, 18997 (2026)

    2026

  45. [53]

    M., Park, H

    Lee, S. M., Park, H. S., Lee, J., Kim, J. and Bang, J., Quantum State Learning via Single-Shot Measurements, Physical Review Letters126, 170504 (2021)

    2021

  46. [54]

    and Li, T.,Neural network assisted high- spatial-resolution polarimetry with non-interleaved chi- ral metasurfaces, Light: Science & Applications12, 288 (2023)

    Chen, C., Xiao, X., Ye, X., Sun, J., Ji, J., Yu, R., Song, W., Zhu, S. and Li, T.,Neural network assisted high- spatial-resolution polarimetry with non-interleaved chi- ral metasurfaces, Light: Science & Applications12, 288 (2023). 10

    2023

  47. [55]

    Echeverr´ ıa-Alar, S., Clerc, M. G. and Bordeu, I.,Emer- gence of disordered branching patterns in confined chi- ral nematic liquid crystals, Proceedings of the National Academy of Sciences120, e2221000120 (2023)

    2023

  48. [56]

    Chang, S.-s.et al.,Electrical tuning of branched flow of light, Nature Communications15, 197 (2024)

    2024

  49. [57]

    and Cardano, F.,Retrieving space-dependent polariza- tion transformations via near-optimal quantum process tomography, Optics Express31, 31698 (2023)

    Di Colandrea, F., Amato, L., Schiattarella, R., Dauphin, A. and Cardano, F.,Retrieving space-dependent polariza- tion transformations via near-optimal quantum process tomography, Optics Express31, 31698 (2023)

    2023

  50. [58]

    A., Meretska, M

    Zaidi, A., Rubin, N. A., Meretska, M. L., Li, L. W., Dorrah, A. H., Park, J.-S. and Capasso, F.,Metasurface- enabled single-shot and complete Mueller matrix imaging, Nature Photonics18, 704 (2024). 11 Supplementary Material for: Single-acquisition tomography of photonic qubits...

    2024

Pith tools

Reviewed July 12, 2026 · model on record in the stance chip above.