Pith. sign in

REVIEW 3 major objections 5 minor 48 references

Efficient Experimental Qudit State Estimation via Point Tomography

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Point tomography experimentally reaches an estimation infidelity of 3.8/N, close to the Gill-Massar bound of 3/N for four-dimensional quantum states, using a single seven-outcome generalized measurement.

desk verdict First experimental demonstration of point tomography: a single seven-outcome POVM yields infidelity scaling close to the Gill-Massar bound, though the headline 3.8/N coefficient rests on a white-noise purity parameter with no reported uncertainty. read the letter →

arxiv 2412.14915 v1 pith:6OLIPG5G submitted 2024-12-19 quant-ph

D. Martínez , L. Pereira , K. Sawada , P. González , J. Cariñe , M. Muñoz , A. Delgado , E. S. Gómez
show 2 more authors
S. P. Walborn G. Lima
This is my paper · ORCID
classification quant-ph MSC 81P1581P50 PACS 03.65.Wj42.50.Ex
keywords quantumstateestimationpointtomographyFisher-symmetricmeasurementsGill-MassarboundquditsmulticoreopticalfiberPOVMsingle-setting
topics The Measurement Problem
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

Point tomography is a state-estimation strategy for the common situation in high-precision experiments where a device is supposed to prepare a known target state and the true state differs only by small systematic deviations. This paper reports the first experimental demonstration of the strategy, using multicore optical fibers to prepare four-dimensional photonic qudits and to implement a single seven-outcome generalized measurement (a POVM). The central quantitative claim is that the infidelity of the estimated state decreases as $3.8/N$, close to the fundamental Gill-Massar bound of $3/N$ for $d=4$, even with ensembles as small as $N=50$. The claim matters because it suggests near-optimal single-setting precision is experimentally reachable, and because the method needs only $2d-1$ measurement outcomes rather than the $\sim 4d-3$ of previous near-optimal schemes, improving the outlook for higher-dimensional systems.

What carries the argument

The central object is a Fisher-symmetric measurement: a rank-1 POVM with $2d-1$ elements $\{|\phi_\eta\rangle\langle\phi_\eta|\}$ around a fiducial state $|0\rangle$ whose classical Fisher information is spread uniformly over the $d-1$ complex deviation parameters, which happens when the matrix $C_{j,k}=\sum_\eta a^j_\eta a^k_\eta$ ($j,k=1,\dots,d-1$) has zero norm. Such a measurement saturates the Gill-Massar bound on infidelity while using only $2d-1$ outcomes instead of the $\sim 4d-3$ needed by previous locally optimal schemes. The experiment approximates this through a $7\times 7$ multicore-fiber multiport beam splitter, selecting among the 35 possible four-input POVM families the one minimizing $\|C\|$ (found at $\approx 0.63$, below the Haar-random average $\approx 0.923$), and reconstructs states by maximum-likelihood estimation. The nonzero residual norm is what keeps the achieved $3.8/N$ slightly above the bound $3/N$.

What would settle it

Run independent full process tomography of the preparation and measurement stages to reconstruct the actual states without assuming the white-noise form, then recompute the infidelity of the seven-outcome estimates against those references; if the fitted coefficient moves well away from $3.8/N$ or the $1/N$ scaling breaks, the central claim fails.

Watch

Extended reading notes

Core claim

The paper claims that point tomography is experimentally viable: a seven-outcome rank-1 POVM built from a $7\times 7$ multiport beam splitter, with four input modes connected, estimates a state at angular parameter $\theta=10^{-2}$ from the fiducial state with infidelity scaling $3.8/N$, against the Gill-Massar limit $3/N$. The implemented measurement is not exactly Fisher-symmetric—the matrix $C$ with entries $C_{j,k}=\sum_{\eta=1}^{7} a^j_\eta a^k_\eta$ has norm $\|C\|\approx 0.63$ rather than zero—yet the estimated precision stays close to the bound. For states farther from the fiducial state ($\theta=10^{-1}$ and $2\times 10^{-1}$), small-ensemble infidelities still track the bound while large-ensemble results plateau, indicating where systematic errors rather than finite statistics dominate. All reported infidelities are evaluated against mixed states $\rho_i=\lambda|\psi_i\rangle\langle\psi_i|+(1-\lambda)I/4$ with a single purity $\lambda=0.987$, assumed to capture preparation and measurement noise.

Load-bearing premise

The load-bearing premise is that the prepared states are exactly the white-noise mixtures $\rho_i=\lambda|\psi_i\rangle\langle\psi_i|+(1-\lambda)I/4$ with a single fixed purity $\lambda=0.987$; if the real noise is not white or $\lambda$ is inaccurate, the reported infidelities, the fitted $3.8/N$, and the claimed closeness to the Gill-Massar bound all shift.

Editorial extensions

If this is right

  • A single seven-outcome measurement estimates a four-dimensional near-fiducial state with infidelity $3.8/N$, about 27% above the Gill-Massar bound $3/N$.
  • High-precision state estimation no longer needs adaptive protocols or $d^2$ separate settings; one fixed POVM suffices near the fiducial state.
  • The measurement-outcome count scales as $2d-1$ instead of $\sim 4d-3$, so the resource advantage grows with dimension.
  • A non-exact Fisher-symmetric measurement ($\|C\|\approx 0.63$) still performs close to the bound, so moderate implementation imperfections need not destroy the advantage.
  • For states farther from the fiducial state, small ensembles still approach the bound while large ensembles are limited by systematic errors, defining the practical neighborhood where point tomography is accurate.

Reading between the lines

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

  • A direct test implied by the residual norm is to search the 35 POVM families for configurations with smaller $\|C\|$ and check whether the infidelity coefficient moves from 3.8 toward 3; the paper does not make this prediction.
  • Independently calibrating $\lambda$ by full tomography of the prepared states, rather than assuming $\lambda=0.987$, would turn the reported agreement into a direct measurement; the paper gives no uncertainty for $\lambda$.
  • If the $2d-1$ outcome count extends to larger $d$, point tomography becomes an attractive default for platforms whose dominant errors are preparation drift rather than readout shot noise, because it avoids adaptive feedback and repeated settings.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports an experimental demonstration of point tomography for four-dimensional photonic qudits. The authors prepare path-encoded states with a multicore-fiber platform, implement a seven-outcome rank-1 POVM approximating a Fisher-symmetric measurement, and estimate the states via maximum likelihood. For the state closest to the fiducial state, they fit the infidelity as 3.8/N, close to the Gill-Massar bound of 3/N for d=4, and they further show degradation for states farther from the fiducial state. The central claim is that a single few-outcome measurement can achieve near-optimal estimation precision in the neighborhood of a known target state.

Significance. If the quantitative claim is substantiated, this is a valuable experimental milestone: it would demonstrate that a single seven-outcome POVM can estimate a d=4 pure state with precision close to the Gill-Massar limit, while requiring only 2d-1 outcomes instead of the roughly 4d-3 outcomes needed in other approaches. The paper has clear strengths: it uses a well-characterized multicore-fiber platform, provides the full 7x7 MBS matrix and all 35 feasible POVM families in the Supplemental Material, compares the chosen POVM against a Haar-random baseline, and reports bootstrap-based error bars. The Gill-Massar benchmark and the Fisher-symmetric-measurement theory are external references, so there is no circularity concern. However, the headline 3.8/N coefficient is computed against a white-noise reference state whose purity lambda is stated without uncertainty or independent calibration, and the systematic-error treatment is not specified. These omissions are load-bearing because they directly enter the infidelity values that are compared to the 3/N bound.

major comments (3)
  1. [Results, second paragraph] The reference state is written as rho_i = lambda |psi_i><psi_i| + (lambda-1) I/d, which is not a valid density matrix for lambda=0.987: its trace is 2lambda-1 = 0.974. This is presumably a typo for (1-lambda) I/d, but as written the model is non-normalized and the infidelity values are undefined. Even after correcting the formula, no uncertainty or independent calibration is given for lambda. Because IF = 1 - F(|psi~><psi~|, rho_i) is computed against this model state, the reported 3.8/N coefficient and the claimed closeness to 3/N are directly contingent on this single number; a shift of lambda by 0.005 changes the infidelity floor by about 0.00375, which is comparable to 3.8/N at N=1000. Please provide an independent calibration of lambda, its uncertainty, the raw count data, and either a fit with lambda as a free parameter or a sensitivity analysis over lambda.
  2. [Results, third paragraph and Fig. 2 caption] The sentence 'We also account for systematic errors in our error model' is not supported by any specification. The phase-drift feedback and the manual intensity-modulator settings are described only qualitatively, and no systematic error budget for phase or intensity settings is given. As a result, the bootstrap error bars reflect only statistical fluctuations and cannot by themselves establish that the experimental infidelity is close to 3/N. Please state the systematic error model explicitly, quantify the phase and intensity errors, and show how these errors enter the red model line and the shaded region.
  3. [Results, Fig. 2a] The fit yielding 3.8/N is quoted without the fitted N-range, the fit function, the uncertainty on the coefficient, or a goodness-of-fit measure. Moreover, because rho_i is mixed with 1-lambda = 0.013, the infidelity has a floor (1-lambda)(d-1)/d = 0.00975; a pure 3.8/N curve crosses below this floor at N approximately 390. The text does not state whether the plotted range extends beyond N=390, so the reader cannot check whether the fit was performed in a regime where the floor is negligible. Please report the ensemble sizes, the fit details, and the data points (or a table), and justify the comparison to the 3/N bound over the fitted range.
minor comments (5)
  1. [Abstract and Results] The phrase 'systemic errors' should be 'systematic errors'; it appears in the abstract and in the Results section.
  2. [Experiment section] The sentence 'the crosstalk between them is depreciable' should presumably read 'negligible'.
  3. [Equation (1) and Supplemental Material] The notation is inconsistent: Eq. (1) of the main text appears to use a scalar theta (with a square-root factor), while the Supplemental Material uses complex parameters theta_j. Please unify the notation and define the parametrization precisely.
  4. [Results, second paragraph] The fidelity F(|psi~><psi~|, rho_i) is not explicitly defined; please state whether it is the squared fidelity or the Uhlmann fidelity, since the comparison with the Gill-Massar bound depends on the convention.
  5. [Supplemental Material, Eq. (8)] The expression for Q_theta appears to be missing a Hermitian conjugation on some inner products; please check and correct this formula.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the fitted 3.8/N is an empirical benchmark against the external Gill-Massar bound, and self-citations are confined to hardware and context, not to the Fisher-symmetric theory being tested.

full rationale

The claimed chain is: (i) point-tomography and Fisher-symmetric measurement theory are taken from Refs [17,23] by Li et al. and by Zhu and Hayashi, which are not authored by this group; (ii) the experimental multiport beam-splitter platform comes from the group's earlier work Refs [24,25], which provides characterized unitaries with stated fidelities; (iii) measured counts are processed by maximum likelihood; (iv) infidelity is plotted against ensemble size and compared with the external Gill-Massar limit 3/N from Ref [9]; and (v) a fit to the measured points yields the reported 3.8/N. Nothing in the paper's equations defines the fitted coefficient in terms of the Fisher-symmetric condition C=0 or in terms of the Gill-Massar bound; the coefficient is explicitly presented as 'a fit of the experimental results,' so it is not a prediction forced by construction. The self-citations to Refs [24,25] support the hardware and are independent experimental characterizations, while the FSM selection criterion from Ref [17] is used only to choose among the 35 feasible POVMs, with ||C|| approximately 0.63, and the closeness to the bound is then measured rather than assumed. The main caveat is the unquantified white-noise purity lambda=0.987 used to define the reference states rho_i; the paper gives no uncertainty or independent calibration for lambda and states 'We also account for systematic errors in our error model' without specifying them. This limits the absolute scale of the infidelities and hence the fitted 3.8/N, but it is a calibration and robustness concern, not a circular reduction: the infidelities and the fitted slope are not defined to equal the theory's predicted value. The score 2 reflects the presence of minor self-citations to the group's own hardware papers while the central derivation and benchmark remain independent.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim depends on the noise model (λ), the fitted scaling coefficient, the hardware characterization from prior work, and the small-θ premise of point tomography. No new physical entities are introduced.

free parameters (2)
  • White-noise purity λ = 0.987
    Introduced in the Results to describe preparation and measurement noise; defines the reference states ρ_i = λ|ψ_i⟩⟨ψ_i| + (1−λ)I/4 and the 'best achievable' red curve. No fitting procedure or uncertainty is given.
  • Reported infidelity scaling coefficient = 3.8
    Obtained by fitting the infidelity-vs-N data for |ψ1⟩; reported as 3.8/N and compared with the theoretical 3/N. No confidence interval is provided.
assumptions (4)
  • ad hoc to paper The true prepared states are well described by ρ_i = λ|ψ_i⟩⟨ψ_i| + (1−λ)I/4 with λ=0.987
    Used to compute all reported infidelities and the reference error model; if the noise is not white or λ is wrong, the reported numbers change.
  • domain assumption The implemented POVM is correctly characterized by the 7×7 matrix U7 from Ref [24] together with the phase settings; near-Fisher-symmetric POVM with ||C||≈0.63 behaves like a Fisher-symmetric measurement
    The experiment relies on the MBS unitary characterization from prior work and on the robustness of point tomography to imperfect Fisher symmetry; this is tested only for the three states reported.
  • domain assumption The states to be estimated lie in the small-θ neighborhood of the fiducial state |0⟩, as in Eq. (1)
    Central premise of point tomography; violated increasingly for θ=0.1 and θ=0.2, which the paper acknowledges as reduced precision.
  • standard math Standard quantum estimation theory (quantum Cramér-Rao, Gill-Massar inequality)
    Used in the supplemental material to define FSM and the GM bound; standard results from Refs [9,41-46].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Efficient Experimental Qudit State Estimation via Point Tomography." pith.science (2026). https://pith.science/paper/6OLIPG5G

@misc{pith2026241214915,
  author       = {Pith},
  title        = {Pith review of: Efficient Experimental Qudit State Estimation via Point Tomography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6OLIPG5G}},
  note         = {Machine review of arXiv:2412.14915}
}
abstract

Point tomography is a new approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target state that their device should prepare, except that intrinsic systematic errors will create small discrepancies in the state actually produced. By introducing a new kind of informationally complete measurement, dubbed Fisher-symmetric measurements, point tomography determines deviations from the expected state with optimal efficiency. In this method, the number of outcomes of a measurement saturating the Gill-Massar limit for reconstructing a $d$-dimensional quantum states can be reduced from $\sim 4d-3$ to only $2d-1$ outcomes. Thus, providing better scalability as the dimension increases. Here we demonstrate the experimental viability of point tomography. Using a modern photonic platform constructed with state-of-the-art multicore optical fiber technology, we generate 4-dimensional quantum states and implement seven-outcome Fisher-symmetric measurements. Our experimental results exhibit the main feature of point tomography, namely a precision close to the Gill-Massar limit with a single few-outcome measurement. Specifically, we achieved a precision of $3.8/N$ while the Gill-Massar limit for $d=4$ is $3/N$ ($N$ being the ensemble size).

Figures

Figures reproduced from arXiv: 2412.14915 by the authors.

Figure 1
Figure 1. FIG. 1. Experimental setup. In the preparation stage, single photon states are generated with a CW-laser, an attenuator (Att), and an [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Experimental results. Insets a), b), and c) are log-log plots for states [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 43 canonical work pages

  1. [1]

    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

  2. [2]

    Szczykulska, T

    M. Szczykulska, T . Baumgratz, and A. Datta, Multi-parameter quantum metrology , Advances in Physics: X1, 621 (2016)

    work page 2016

  3. [3]

    Albarelli, M

    F . Albarelli, M. Barbieri, M. G. Genoni, and I. Gianani, A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging, Physics Letters A 384, 126311 (2020)

    work page 2020

  4. [4]

    B. P . Lanyon, M. Barbieri, M. P . Almeida, T . Jennewein, T . C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, Simplifying quantum logic using higher- dimensional Hilbert spaces, Nature Physics 5, 134 (2009)

    work page 2009

  5. [5]

    Bocharov, M

    A. Bocharov, M. Roetteler, and K. M. Svore, Factoring with qutrits: Shor’s algorithm on ternary and metaplectic quantum architectures, Physical Review A 96, 012306 (2017)

    work page 2017

  6. [6]

    Babazadeh, M

    A. Babazadeh, M. Erhard, F . Wang, M. Malik, R. Nouroozi, M. Krenn, and A. Zeilinger, High-Dimensional Single- Photon Quantum Gates: Concepts and Experiments, Physical Review Letters 119, 180510 (2017)

    work page 2017

  7. [7]

    Muralidharan, C.-L

    S. Muralidharan, C.-L. Zou, L. Li, J. Wen, and L. Jiang, Overcoming erasure errors with multilevel systems, New Journal of Physics 19, 013026 (2017)

    work page 2017

  8. [8]

    M. M. Taddei, J. Cariñe, D. Martínez, T . García, N. Guerrero, A. A. Abbott, M. Araújo, C. Branciard, E. S. Gómez, S. P . Walborn, L. Aolita, and G. Lima, Computational Advantage from the Quantum Superposition of Multiple Temporal Orders of Photonic Gates, PRX Quantum 2, 010320 (2021)

    work page 2021

Show all 48 references
  1. [9]

    R. D. Gill and S. Massar, State estimation for large ensembles, Physical Review A 61, 042312 (2000)

    2000

  2. [10]

    Ferrie, Self-Guided Quantum Tomography, Physical Review Letters 113, 190404 (2014)

    C. Ferrie, Self-Guided Quantum Tomography, Physical Review Letters 113, 190404 (2014)

    2014

  3. [11]

    D. H. Mahler, L. A. Rozema, A. Darabi, C. Ferrie, R. Blume- Kohout, and A. M. Steinberg, Adaptive Quantum State Tomography Improves Accuracy Quadratically, Physical Review Letters 111, 183601 (2013)

    2013

  4. [12]

    S. S. Straupe, Adaptive quantum tomography , JETP Letters 104, 510 (2016)

    2016

  5. [13]

    G. I. Struchalin, E. V . Kovlakov, S. S. Straupe, and S. P . Kulik, Adaptive quantum tomography of high-dimensional bipartite systems, Physical Review A 98, 032330 (2018)

    2018

  6. [14]

    Huszár and N

    F . Huszár and N. Houlsby , Adaptive Bayesian quantum tomography , Physical Review A85, 052120 (2012)

    2012

  7. [15]

    Pereira, L

    L. Pereira, L. Zambrano, J. Cortés-Vega, S. Niklitschek, and A. Delgado, Adaptive quantum tomography in high dimensions, Physical Review A 98, 012339 (2018)

    2018

  8. [16]

    J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric informationally complete quantum measurements, Journal of Mathematical Physics 45, 2171 (2004)

    2004

  9. [17]

    N. Li, C. Ferrie, J. A. Gross, A. Kalev, and C. M. Caves, Fisher-Symmetric Informationally Complete Measurements for Pure States, Physical Review Letters116, 180402 (2016)

    2016

  10. [18]

    D. M. Appleby , H. B. Dang, and C. A. Fuchs, Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States, Entropy 16, 1484 (2014)

    2014

  11. [19]

    ˇReháˇcek, B.-G

    J. ˇReháˇcek, B.-G. Englert, and D. Kaszlikowski, Minimal qubit tomography , Physical Review A70, 052321 (2004)

    2004

  12. [20]

    W . M. Pimenta, B. Marques, M. A. Carvalho, M. R. Barros, J. G. Fonseca, J. Ferraz, M. Terra Cunha, and S. Pádua, Minimal state tomography of spatial qubits using a spatial light modulator, Optics Express 18, 24423 (2010)

    2010

  13. [21]

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

    2015

  14. [22]

    Stricker, M

    R. Stricker, M. Meth, L. Postler, C. Edmunds, C. Ferrie, R. Blatt, P . Schindler, T . Monz, R. Kueng, and M. Ringbauer, Experimental Single-Setting Quantum State Tomography, PRX Quantum 3, 040310 (2022)

    2022

  15. [23]

    Zhu and M

    H. Zhu and M. Hayashi, Universally Fisher-Symmetric Informationally Complete Measurements, Physical Review Letters 120, 030404 (2018)

    2018

  16. [24]

    Cariñe, G

    J. Cariñe, G. Cañas, P . Skrzypczyk, I. Šupi ´c, N. Guerrero, T . Garcia, L. Pereira, M. A. S. Prosser, G. B. Xavier, A. Delgado, S. P . Walborn, D. Cavalcanti, and G. Lima, Multi- core fiber integrated multi-port beam splitters for quantum information processing, Optica 7, 542 (2020)

    2020

  17. [25]

    Martínez, E

    D. Martínez, E. S. Gómez, J. Cariñe, L. Pereira, A. Delgado, S. P . Walborn, A. Tavakoli, and G. Lima, Certification of a non- projective qudit measurement using multiport beamsplitters, Nature Physics 19, 190 (2023). 6

    2023

  18. [26]

    Pirandola, U

    S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T . Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V . C. Usenko, G. Vallone, P . Villoresi, and P . Wallden, Advances in quantum cryptography ,...

    2020

  19. [27]

    A. K. Fedorov, N. Gisin, S. M. Beloussov, and A. I. Lvovsky , Quantum computing at the quantum advantage threshold: a down-to-business review (2022), arXiv:2203.17181

    2022 arXiv

  20. [28]

    See supplemental material

  21. [29]

    D. J. Richardson, J. M. Fini, and L. E. Nelson, Space- division multiplexing in optical fibres, Nature Photonics 7, 354 (2013)

    2013

  22. [30]

    G. B. Xavier and G. Lima, Quantum information processing with space-division multiplexing optical fibres, Communications Physics 3, 9 (2020)

    2020

  23. [31]

    Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits, npj Quantum Information 3, 1 (2017)

    2017

  24. [32]

    Cañas, N

    G. Cañas, N. Vera, J. Cariñe, P . González, J. Cardenas, P . W . R. Connolly , A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P . Villoresi, T . F . Da Silva, G. B. Xavier, and G. Lima, High-dimensional decoy-state quantum key distribution over multicore telecommunicatio...

    2017

  25. [33]

    Sarmiento, S

    S. Sarmiento, S. Etcheverry , J. Aldama, I. H. López, L. T . Vidarte, G. B. Xavier, D. A. Nolan, J. S. Stone, M. J. Li, D. Loeber, and V . Pruneri, Continuous-variable quantum key distribution over a 15 km multi-core fiber, New Journal of Physics 24, 063011 (2022)

    2022

  26. [34]

    Zahidy , D

    M. Zahidy , D. Ribezzo, C. De Lazzari, I. Vagniluca, N. Biagi, R. Müller, T . Occhipinti, L. K. Oxenløwe, M. Galili, T . Hayashi, D. Cassioli, A. Mecozzi, C. Antonelli, A. Zavatta, and D. Bacco, Practical high-dimensional quantum key distribution protocol over deployed multico...

    2024

  27. [35]

    H. J. Lee, S.-K. Choi, and H. S. Park, Experimental Demonstration of Four-Dimensional Photonic Spatial Entanglement between Multi-core Optical Fibres, Scientific Reports 7, 4302 (2017)

    2017

  28. [36]

    H. J. Lee and H. S. Park, Generation and measurement of arbitrary four-dimensional spatial entanglement between photons in multicore fibers, Photonics Research 7, 19 (2019)

    2019

  29. [37]

    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,...

    2021

  30. [38]

    E. S. Gómez, S. Gómez, I. Machuca, A. Cabello, S. Pádua, S. P . Walborn, and G. Lima, Multidimensional Entanglement Generation with Multicore Optical Fibers, Physical Review Applied 15, 034024 (2021)

    2021

  31. [39]

    Abarzúa, C

    H. Abarzúa, C. Melo, S. E. Restrepo, S. Vergara, D. Sbarbaro, G. Cañas, G. Lima, G. Saavedra, and J. Cariñe, Adaptive-Step Perturb-and-Observe Algorithm for Multidimensional Phase Noise Stabilization in Fiber-Based Multi-Arm Mach–Zehnder Interferometers, Algorithms 17, 534 (2024)

    2024

  32. [40]

    Shang, Z

    J. Shang, Z. Zhang, and H. K. Ng, Superfast maximum- likelihood reconstruction for quantum tomography , Physical Review A 95, 062336 (2017)

    2017

  33. [41]

    C. W . Helstrom, Quantum detection and estimation theory , Journal of Statistical Physics 1, 231 (1969)

    1969

  34. [42]

    V . P . Belavkin, Generalized uncertainty relations and efficient measurements in quantum systems, Theoretical and Mathematical Physics 26, 213 (1976)

    1976

  35. [43]

    Yuen and M

    H. Yuen and M. Lax, Multiple-parameter quantum estimation and measurement of nonselfadjoint observables, IEEE Transactions on Information Theory 19, 740 (1973)

    1973

  36. [44]

    M. G. A. Paris, Quantum estimation for quantum technology , International Journal of Quantum Information 07, 125 (2009)

    2009

  37. [45]

    Holevo,Probabilistic and Statistical Aspects of Quantum Theory (Edizioni della Normale, Pisa, 2011)

    A. Holevo,Probabilistic and Statistical Aspects of Quantum Theory (Edizioni della Normale, Pisa, 2011)

    2011

  38. [46]

    J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum Fisher information matrix and multiparameter estimation, Journal of Physics A: Mathematical and Theoretical 53, 023001 (2020)

    2020

  39. [47]

    Muñoz, L

    M. Muñoz, L. Pereira, S. Niklitschek, and A. Delgado, Complex Field Formulation of the Quantum Estimation Theory (2022), arXiv:2203.03064

    2022 arXiv

  40. [48]

    Mezzadri, How to generate random matrices from the classical compact groups, Notices of the American Mathematical Society 54, 592 (2007)

    F . Mezzadri, How to generate random matrices from the classical compact groups, Notices of the American Mathematical Society 54, 592 (2007). 7 SUPPLEMENTAL MATERIAL Fisher-Symmetric measurements Here, we present the Fisher-symmetric measurements (FSM) introduced in Ref. [17]....

    2007

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.