pith. sign in

arxiv: 2604.06528 · v1 · submitted 2026-04-07 · 🪐 quant-ph

High-Dimensional Quantum Photonics: Roadmap

Mehul Malik , Micheal Kues , Takuya Ikuta , Hiroki Takesue , Daniele Bajoni , David J. Moss , Roberto Morandotti , Andrew Forbes
show 25 more authors
Stephen Walborn Ebrahim Karimi Yunhong Ding Stefano Paesani Caterina Vigliar Benjamin Brecht Christine Silberhorn Fr\'ed\'eric Bouchard Micha{\l} Karpi\'nski Benjamin Sussman Joseph M. Lukens Yaron Bromberg Robert Fickler Taira Giordani Fabio Sciarrino Yun Zheng Jianwei Wang Marcus Huber Armin Tavakoli Roope Uola Nicolas Brunner Nicolai Friis Natalia Herrera Valencia Jacquiline Romero Will McCutcheon
This is my paper

Pith reviewed 2026-05-10 18:23 UTC · model grok-4.3

classification 🪐 quant-ph
keywords high-dimensional quantum photonicsphotonic degrees-of-freedomquantum states of lightentangled photonsquantum communicationquantum information processingroadmap
0
0 comments X

The pith

Research in high-dimensional quantum photonics has advanced independently across photonic degrees-of-freedom, requiring a unified roadmap to connect them for next-generation quantum technologies.

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

The paper surveys methods to generate, manipulate, and use multimode photonic degrees-of-freedom such as spatial, temporal, and spectral structures to encode multi-level quantum states in single and entangled photons. It establishes that these states have enabled noise-robust tests of quantum mechanics, error-resilient communication, and efficient information processing with advantages over qubit approaches. However, progress has occurred with little exchange between different degrees-of-freedom or between experiment and theory. The roadmap reviews early work and current techniques, outlines outstanding challenges for each, and identifies shared issues in distribution, measurement, and manipulation. A sympathetic reader would care because bridging these gaps could accelerate practical integration into scalable quantum platforms.

Core claim

High-dimensional quantum states of light encoded in time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have supported specific applications in fundamental tests and quantum technologies, yet independent development across these areas and between theory and experiment creates a gap that this roadmap addresses by surveying state-of-the-art methods, identifying challenges, and highlighting interconnections for future platforms.

What carries the argument

The roadmap as a comparative survey tool that maps progress and shared challenges across photonic degrees-of-freedom to enable interconnections in distribution, measurement, and manipulation.

Load-bearing premise

That surveying existing work and outlining interconnections across degrees-of-freedom will effectively bridge the independent progress gap, rather than requiring fundamentally new breakthroughs.

What would settle it

An experimental demonstration that no common challenges or transferable techniques exist between any two photonic degrees-of-freedom, such as time-bin and spatial-mode encodings, would undermine the roadmap's premise of useful unification.

Figures

Figures reproduced from arXiv: 2604.06528 by Andrew Forbes, Armin Tavakoli, Benjamin Brecht, Benjamin Sussman, Caterina Vigliar, Christine Silberhorn, Daniele Bajoni, David J. Moss, Ebrahim Karimi, Fabio Sciarrino, Fr\'ed\'eric Bouchard, Hiroki Takesue, Jacquiline Romero, Jianwei Wang, Joseph M. Lukens, Marcus Huber, Mehul Malik, Micha{\l} Karpi\'nski, Micheal Kues, Natalia Herrera Valencia, Nicolai Friis, Nicolas Brunner, Robert Fickler, Roberto Morandotti, Roope Uola, Stefano Paesani, Stephen Walborn, Taira Giordani, Takuya Ikuta, Will McCutcheon, Yaron Bromberg, Yunhong Ding, Yun Zheng.

Figure 1
Figure 1. Figure 1: Generation and measurement of time-energy entangled qutrits using three-arm [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Measurement of a high-dimensional time-bin state using (a) cascaded delay [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: All projective measurements in the Fourier basis. (a) Diagram of the tree [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Practical phase encoding in the subspace of a four-dimensional time-bin [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) The concept of how a four-dimensional time-bin state is informationally [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Experimental setup for measuring the complete set of MUBs for a four [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Deterministic measurement of a high-dimensional time-bin state in the Hadamard [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Measurement of a high-dimensional time-bin state using dispersive optics [ [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Difference between the coincidence fringes of four-dimensional time-bin [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Experiment certifying the noise-robustness of a high-dimensional time-bin [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Scheme for the generation of frequency-bin-encoded heralded single [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a) Scheme from Ref. [76] for the programmable generation of linear combinations of the |00⟩ and |11⟩ states including the maximally entangled Bell states |Φ+ ⟩ and |Φ− ⟩. The top row (a–d) shows the integrated circuit geometry along with the excitation patterns for all four states. The source is composed of two microring resonators that can be independently and selectively excited via a Mach-Zehnder inte… view at source ↗
Figure 13
Figure 13. Figure 13: (a) Scheme for the demonstration of deterministic CNOT operation between [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Top panel: An example of a two-photon high-dimensional state expressed in [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The modern toolkit for the creation of transverse modes as quantum states [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Definition of high-dimensional path encodings. [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: A. Typical geometry of a silicon waveguide with SiO2 cladding, and the [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Mach-Zehnder interferometer networks for realizing universal qubit/qudit [PITH_FULL_IMAGE:figures/full_fig_p032_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Demonstration of the generation and manipulation of path-encoded qudits from [PITH_FULL_IMAGE:figures/full_fig_p035_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Schematic visualization of the spectral amplitudes [PITH_FULL_IMAGE:figures/full_fig_p038_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The joint spectral amplitude 𝐹(𝜔s , 𝜔i) (purple) is the product of the pump envelope 𝛼 (blue) and phase matching function 𝜙 (teal). It is decomposed into pairs of biorthogonal Schmidt modes { 𝑓 𝑗(𝜔s)}, {𝑔𝑗(𝜔i)} with weights given by the Schmidt coefficients { √︁ 𝜆 𝑗 }. The visualization shows the first three terms of the decomposition (𝑗 = 0, 1, 2). enabling integration into photonic quantum networks [314… view at source ↗
Figure 22
Figure 22. Figure 22: Schematic of an mQPG. A multi-TM signal (purple) is coupled into the mQPG [PITH_FULL_IMAGE:figures/full_fig_p041_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Visualization of a frequency-encoded quantum information network based [PITH_FULL_IMAGE:figures/full_fig_p042_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Manipulation of time-bin qudits across different timescales. (a–d) Trains of optical pulses illustrating decreasing time-bin separations from > 10 ns to ∼ 1 ns, ∼ 100 ps, and < 10 ps. (e–h) Representative architectures for realizing the corresponding time-delayed interferometers, respectively, fiber loops, free-space delay lines, integrated on-chip delay lines, and birefringent-crystal delays with path di… view at source ↗
Figure 25
Figure 25. Figure 25: Frequency-bin processing with frequency-mode mixing for projective superpo [PITH_FULL_IMAGE:figures/full_fig_p051_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Spectral Hong-Ou-Mandel interference with dependently (a) and independently [PITH_FULL_IMAGE:figures/full_fig_p052_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Hyperentanglement scheme for frequency and time, allowing with coherent [PITH_FULL_IMAGE:figures/full_fig_p053_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Temporal shaping of frequency-bin-entangled qutrits with an integrated [PITH_FULL_IMAGE:figures/full_fig_p054_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Frequency-bin entanglement-based quantum key distribution. A basis state [PITH_FULL_IMAGE:figures/full_fig_p055_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Current approaches for spatial-mode qudit manipulation include a) multi-plane [PITH_FULL_IMAGE:figures/full_fig_p058_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Reported distances and dimensions 𝑑 for the distribution of transverse spatial modes. Free-space laboratory demonstrations have achieved the highest dimensions to date, while fiber-based systems enable long-distance transmission but are currently limited to 𝑑 = 4. The distribution of higher-dimensional states over long distances remains an outstanding challenge. transverse modes through fibers. Distributi… view at source ↗
Figure 32
Figure 32. Figure 32: Path-encoding architectures. (a) Illustration of the Reck decomposition [257], in which the blue squares represent tunable beam-splitters and phase-shifters. (b) The Clements decomposition [258]. (c) Tunable beam-splitters constructed from MZIs featuring a single internal phase-shifter and an external phase-shifter to constitute a full unit cell. (d) A symmetric MZI variant that uses two internal phase sh… view at source ↗
Figure 33
Figure 33. Figure 33: Complex states generation and quantum computing. a) and b): on-chip multi-mode interferometers enable the generation of complex multiphoton entangled states and QIP, driven by off-chip quantum-dot single-photon sources. c) very-large-scale integrated quantum graph device. Multiphoton high-dimensional genuine entanglement could be generated and processed with on-chip parametric sources and MZI arrays. d) t… view at source ↗
Figure 34
Figure 34. Figure 34: Distribution of quantum states between chips. a) and b): Superposition states transmission via one-to-one mapping from on-chip paths to MCF spatial modes. c) and d): Entangled states distribution by using coherent DoF conversion techniques. e) and f): chip-to-chip quantum state and gate teleportation. Figures from Ref. [674], Ref. [200], Ref. [604], Ref. [675], Ref. [218] and Ref. [605] reproduced without… view at source ↗
Figure 35
Figure 35. Figure 35: Toward modular and hybrid path-encoded integrated photonic platforms. a) The modular photonic quantum processor Aurora envisages off-chip fast modulation and optical delays to enable feed-forward operations. Figure from Ref. [682] reproduced without modifications under CC BY-NC-ND 4.0 license. b) The Jiuzhang 4.0 processor combines path-encoding and temporal-encoding to scale the size of Boson Samplers. F… view at source ↗
Figure 36
Figure 36. Figure 36: (Left) Genuine 𝑁-outcome measurement. (Right) Binarised implementation of 𝑁-outcome measurement based on 𝑁 independent “click or no-click” measurments. Picture taken from Phys. Rev. A 111, 042433 (2025). is also an interesting avenue for future research. Recent works have shown encouraging first results, but a number of key challenges still have to be addressed. Among these is the issue of loopholes that … view at source ↗
read the original abstract

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript is a roadmap for high-dimensional quantum photonics. It surveys techniques for generating, manipulating, and distributing high-dimensional quantum states of light encoded in photonic degrees of freedom including spatial modes, temporal modes, frequency bins, time bins, and waveguide paths. The paper reviews early and state-of-the-art experimental methods, theoretical tools for measurement and certification, outlines outstanding challenges specific to each degree of freedom, and concludes with a discussion of cross-cutting issues in distribution, measurement, and manipulation aimed at integration into next-generation quantum platforms.

Significance. If the survey is comprehensive and the identified interconnections are accurate, the roadmap will be significant for the field. It can serve as a reference that promotes exchange between communities working on different DoFs, highlights shared technical barriers, and guides coordinated progress toward practical high-dimensional quantum technologies that offer noise robustness and higher information capacity compared to qubit encodings.

major comments (2)
  1. [Abstract and §1] Abstract and §1: The central premise that research has 'progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory' is stated without concrete supporting examples or citation clusters in the provided framing; a brief table or paragraph in the introduction listing representative cross-DoF collaborations (or their absence) would strengthen the justification for the roadmap.
  2. [Cross-cutting challenges section] Cross-cutting challenges section: The discussion of shared challenges in distribution, measurement, and manipulation would benefit from explicit cross-DoF comparisons (e.g., loss scaling or certification overhead for spatial vs. frequency-bin encodings) rather than parallel lists; without such side-by-side metrics the claim that these issues 'cut across two or more' DoFs remains qualitative.
minor comments (3)
  1. Ensure that the review of 'state-of-the-art experimental techniques' includes the most recent 2023–2024 results for each DoF, as the field evolves quickly.
  2. Consider adding a summary table comparing key performance metrics (e.g., dimensionality achieved, fidelity, generation rate) across the main DoFs to aid readers.
  3. Clarify the scope: the abstract mentions 'single and entangled photons' but the roadmap should explicitly state whether multi-photon high-dimensional states are covered or deferred.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for the constructive suggestions aimed at strengthening the justification for the roadmap and the cross-cutting analysis. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and §1] Abstract and §1: The central premise that research has 'progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory' is stated without concrete supporting examples or citation clusters in the provided framing; a brief table or paragraph in the introduction listing representative cross-DoF collaborations (or their absence) would strengthen the justification for the roadmap.

    Authors: We agree that explicit examples would better ground the premise. In the revised manuscript we will insert a short paragraph (and, if space permits, a compact table) in Section 1 that cites representative cross-DoF collaborations (e.g., joint spatial-temporal mode experiments and frequency-bin/time-bin hybrid encodings) as well as areas where exchange has remained limited. These additions will be supported by the existing citation clusters already present in the later sections and will not change the overall narrative or length significantly. revision: yes

  2. Referee: [Cross-cutting challenges section] Cross-cutting challenges section: The discussion of shared challenges in distribution, measurement, and manipulation would benefit from explicit cross-DoF comparisons (e.g., loss scaling or certification overhead for spatial vs. frequency-bin encodings) rather than parallel lists; without such side-by-side metrics the claim that these issues 'cut across two or more' DoFs remains qualitative.

    Authors: We accept that side-by-side metrics would make the interconnections more concrete. In the revision we will augment the cross-cutting section with explicit comparisons, including tabulated or bulleted contrasts of loss scaling (e.g., spatial-mode propagation versus frequency-bin transmission) and certification overhead where quantitative literature values exist. For certain aspects, such as manipulation fidelity across platforms, direct numerical metrics are not uniformly reported; we will therefore retain some qualitative discussion but anchor it with specific references and highlight the common technical barriers more sharply. This change will be partial because not every metric can be placed on an identical quantitative footing without introducing new data. revision: partial

Circularity Check

0 steps flagged

No circularity detected in survey roadmap

full rationale

This paper is a literature survey and roadmap that reviews progress in high-dimensional quantum photonics across photonic degrees of freedom, outlines challenges, and discusses cross-cutting issues without any mathematical derivations, predictions, fitted parameters, or original theoretical claims. The central premise—that independent progress creates a gap best addressed by systematic comparison—is a standard function of review articles and is self-contained in the act of surveying existing work; it does not reduce to self-definition, fitted inputs called predictions, or load-bearing self-citations. No equations or derivation chains exist to inspect for circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review and roadmap paper containing no new scientific derivations, fitted parameters, axioms, or postulated entities; all content draws from cited prior literature without introducing independent postulates.

pith-pipeline@v0.9.0 · 5725 in / 1100 out tokens · 40006 ms · 2026-05-10T18:23:33.252022+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Non-Gaussian Entanglement Hierarchy Based on the Schmidt Number

    quant-ph 2026-05 unverdicted novelty 7.0

    Introduces witness E_NG whose ceiling bounds the Gaussian-irreducible Schmidt number, defining a hierarchy of non-Gaussian entanglement in continuous-variable systems.

  2. Second-order moment equivalence of twisted Gaussian Schell model beams and orbital angular momentum eigenmodes

    physics.optics 2026-05 unverdicted novelty 5.0

    Covariance matrices of coherent OAM eigenmodes and TGSM beams share identical structure and zero/nonzero pattern, enabling second-order equivalence under ABCD transformations for arbitrary radial profiles.

Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · cited by 2 Pith papers

  1. [1]

    Bell-type test of energy-time entangled qutrits,

    R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett.93, 010503 (2004)

    work page 2004

  2. [2]

    Bell inequality for position and time,

    J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett.62, 2205–2208 (1989)

    work page 1989

  3. [3]

    Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,

    J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett.82, 2594–2597 (1999)

    work page 1999

  4. [4]

    Bell inequalities for arbitrarily high-dimensional systems,

    D. Collins, N. Gisin, N. Linden,et al., “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002)

    work page 2002

  5. [5]

    Higher dimensional time-energy entanglement,

    D. Lampert Richart, “Higher dimensional time-energy entanglement,” Ph.D. thesis, Ludwig-Maximilians-Universität München (2014)

    work page 2014

  6. [6]

    Experimental implementation of higher dimensional time-energy entanglement,

    D. Richart, Y. Fischer, and H. Weinfurter, “Experimental implementation of higher dimensional time-energy entanglement,” Appl. Phys. B106, 543–550 (2012)

    work page 2012

  7. [7]

    Mutually unbiased measurements for high-dimensional time-bin based photonic states,

    T. Brougham and S. M. Barnett, “Mutually unbiased measurements for high-dimensional time-bin based photonic states,” EPL (Europhysics Lett.104, 30003 (2013)

    work page 2013

  8. [8]

    Tailoring photonic entanglement in high-dimensional Hilbert spaces,

    H. De Riedmatten, I. Marcikic, V. Scarani,et al., “Tailoring photonic entanglement in high-dimensional Hilbert spaces,” Phys. Rev. A69, 050304 (2004)

    work page 2004

  9. [9]

    Quantum secret sharing based on modulated high-dimensional time-bin entanglement,

    H. Takesue and K. Inoue, “Quantum secret sharing based on modulated high-dimensional time-bin entanglement,” Phys. Rev. A74, 012315 (2006)

    work page 2006

  10. [10]

    Exploring energy-time entanglement using geometric phase,

    A. K. Jha, M. Malik, and R. W. Boyd, “Exploring energy-time entanglement using geometric phase,” Phys. Rev. Lett. 101, 180405 (2008)

    work page 2008

  11. [11]

    Enhanced violation of the collins-gisin-linden-massar-popescu inequality with optimized time-bin-entangled ququarts,

    T. Ikuta and H. Takesue, “Enhanced violation of the collins-gisin-linden-massar-popescu inequality with optimized time-bin-entangled ququarts,” Phys. Rev. A93, 022307 (2016)

    work page 2016

  12. [12]

    Quantum key distribution implemented with d-level time-bin entangled photons,

    H. Yu, S. Sciara, M. Chemnitz,et al., “Quantum key distribution implemented with d-level time-bin entangled photons,” Nat. Commun.16, 171 (2025)

    work page 2025

  13. [13]

    Provably secure and high-rate quantum key distribution with time-bin qudits,

    N. T. Islam, C. C. W. Lim, C. Cahall,et al., “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv.3, e1701491 (2017)

    work page 2017

  14. [14]

    Robustandstabledelayinterferometerswithapplicationtod-dimensional time-frequency quantum key distribution,

    N.T.Islam,C.Cahall,A.Aragoneses,etal.,“Robustandstabledelayinterferometerswithapplicationtod-dimensional time-frequency quantum key distribution,” Phys. Rev. Appl.7, 044010 (2017)

    work page 2017

  15. [15]

    Security of quantum key distribution usingd-level systems,

    N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution usingd-level systems,” Phys. Rev. Lett.88, 127902 (2002)

    work page 2002

  16. [16]

    Security proof for quantum key distribution using qudit systems,

    L. Sheridan and V. Scarani, “Security proof for quantum key distribution using qudit systems,” Phys. Rev. A82, 030301 (2010)

    work page 2010

  17. [17]

    Securityofhigh-dimensionalquantumkeydistributionprotocols using Franson interferometers,

    T.Brougham,S.M.Barnett,K.T.McCusker,etal.,“Securityofhigh-dimensionalquantumkeydistributionprotocols using Franson interferometers,” J. Phys. B46, 104010 (2013)

    work page 2013

  18. [18]

    Efficient detection of multidimensional single-photon time-bin superpositions,

    A. Widomski, M. Ogrodnik, and M. Karpiński, “Efficient detection of multidimensional single-photon time-bin superpositions,” Optica11, 926–931 (2024)

    work page 2024

  19. [19]

    Efficient time-bin encoding for practical high-dimensional quantum key distribution,

    I. Vagniluca, B. Da Lio, D. Rusca,et al., “Efficient time-bin encoding for practical high-dimensional quantum key distribution,” Phys. Rev. Appl.14, 014051 (2020)

    work page 2020

  20. [20]

    Scalableimplementationof (𝑑+1) mutuallyunbiasedbasesfor 𝑑-dimensional quantum key distribution,

    T.Ikuta,S.Akibue,Y.Yonezu,etal.,“Scalableimplementationof (𝑑+1) mutuallyunbiasedbasesfor 𝑑-dimensional quantum key distribution,” Phys. Rev. Res.4, L042007 (2022)

    work page 2022

  21. [21]

    Optimal state-determination by mutually unbiased measurements,

    W. K. Wootters and B. D. Fields, “Optimal state-determination by mutually unbiased measurements,” Ann. Phys. 191, 363–381 (1989)

    work page 1989

  22. [22]

    On mutually unbiased bases,

    THOMAS. DURT, B.-G. ENGLERT, INGEMAR. BENGTSSON, and KAROL. ŻYCZKOWSKI, “On mutually unbiased bases,” Int. J. Quantum Inf.08, 535–640 (2010)

    work page 2010

  23. [23]

    OptimalEavesdroppinginQuantumCryptographywithSixStates,

    D.Bruß,“OptimalEavesdroppinginQuantumCryptographywithSixStates,”Phys.Rev.Lett.81,3018–3021(1998)

    work page 1998

  24. [24]

    Programming quantum measurements of time inside a complex medium,

    D. Danese, V. Srivastav, W. McCutcheon,et al., “Programming quantum measurements of time inside a complex medium,” arXiv preprint arXiv:2601.14565 (2026)

    work page arXiv 2026

  25. [25]

    Implementation of quantum state tomography for time-bin entangled photon pairs,

    H. Takesue and Y. Noguchi, “Implementation of quantum state tomography for time-bin entangled photon pairs,” Opt. Express17, 10976 (2009)

    work page 2009

  26. [26]

    Implementationofquantumstatetomographyfortime-binqudits,

    T.IkutaandH.Takesue,“Implementationofquantumstatetomographyfortime-binqudits,”NewJ.Phys.19,013039 (2017)

    work page 2017

  27. [27]

    Four-dimensional entanglement distribution over 100 km,

    T. Ikuta and H. Takesue, “Four-dimensional entanglement distribution over 100 km,” Sci. Rep.8, 817 (2018)

    work page 2018

  28. [28]

    Tomographic reconstruction of time-bin-entangled qudits,

    S. J. Nowierski, N. N. Oza, P. Kumar, and G. S. Kanter, “Tomographic reconstruction of time-bin-entangled qudits,” Phys. Rev. A94, 042328 (2016)

    work page 2016

  29. [29]

    All-optical switching of photonic entanglement,

    M. A. Hall, J. B. Altepeter, and P. Kumar, “All-optical switching of photonic entanglement,” New J. Phys.13, 105004 (2011)

    work page 2011

  30. [30]

    Entanglement-Preserving Photonic Switching: Full Cross-Bar Operation With Quantum Data Streams,

    N. N. Oza, Y.-P. Huang, and P. Kumar, “Entanglement-Preserving Photonic Switching: Full Cross-Bar Operation With Quantum Data Streams,” IEEE Photonics Technol. Lett.26, 356–359 (2014)

    work page 2014

  31. [31]

    Measuring ultrafast time-bin qudits,

    F. Bouchard, K. Bonsma-Fisher, K. Heshami,et al., “Measuring ultrafast time-bin qudits,” Phys. Rev. A107, 022618 (2023)

    work page 2023

  32. [32]

    Time-bin-to-polarization conversion of ultrafast photonic qubits,

    C. Kupchak, P. J. Bustard, K. Heshami,et al., “Time-bin-to-polarization conversion of ultrafast photonic qubits,” Phys. Rev. A96, 053812 (2017)

    work page 2017

  33. [33]

    Terahertz-bandwidth switching of heralded single photons,

    C. Kupchak, J. Erskine, D. England, and B. Sussman, “Terahertz-bandwidth switching of heralded single photons,” Opt. Lett.44, 1427 (2019)

    work page 2019

  34. [34]

    Quantum Communication with Ultrafast Time-Bin Qubits,

    F. Bouchard, D. England, P. J. Bustard,et al., “Quantum Communication with Ultrafast Time-Bin Qubits,” PRX Quantum3, 010332 (2022)

    work page 2022

  35. [35]

    Scalable high-rate, high-dimensional time-bin encoding quantum key distribution,

    N. T. Islam, C. C. W. Lim, C. Cahall,et al., “Scalable high-rate, high-dimensional time-bin encoding quantum key distribution,” Quantum Sci. Technol.4, 035008 (2019)

    work page 2019

  36. [36]

    Generalized measurements by linear elements,

    J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A65, 030301 (2002)

    work page 2002

  37. [37]

    Qudit-Teleportation for photons with linear optics,

    S. K. Goyal, P. E. Boukama-Dzoussi, S. Ghosh,et al., “Qudit-Teleportation for photons with linear optics,” Sci. Rep. 4, 4543 (2014)

    work page 2014

  38. [38]

    High-dimensional quantum key distribution using dispersive optics,

    J. Mower, Z. Zhang, P. Desjardins,et al., “High-dimensional quantum key distribution using dispersive optics,” Phys. Rev. A87, 062322 (2013)

    work page 2013

  39. [39]

    Space-time analogies in optics,

    V. Torres-Company, J. Lancis, and P. Andres, “Space-time analogies in optics,” Prog. Opt.56, 1–80 (2011)

    work page 2011

  40. [40]

    Dispersive fourier transformation for fast continuous single-shot measurements,

    K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics7, 102–112 (2013)

    work page 2013

  41. [41]

    Fiber-assisted single-photon spectrograph,

    M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. letters 34, 2873–2875 (2009)

    work page 2009

  42. [42]

    Pulsed single-photon spectrometer by frequency-to-time mapping using chirped fiber bragg gratings,

    A. O. Davis, P. M. Saulnier, M. Karpiński, and B. J. Smith, “Pulsed single-photon spectrometer by frequency-to-time mapping using chirped fiber bragg gratings,” Opt. Express25, 12804–12811 (2017)

    work page 2017

  43. [43]

    Energy-time entanglement-based dispersive optics quantum key distribution over optical fibers of 20 km,

    X. Liu, X. Yao, H. Wang,et al., “Energy-time entanglement-based dispersive optics quantum key distribution over optical fibers of 20 km,” Appl. Phys. Lett.114, 141104 (2019)

    work page 2019

  44. [44]

    High-dimensional quantum key distribution using energy-time entanglement over 242 km partially deployed fiber,

    J. Liu, Z. Lin, D. Liu,et al., “High-dimensional quantum key distribution using energy-time entanglement over 242 km partially deployed fiber,” Quantum Sci. Technol.9, 015003 (2024)

    work page 2024

  45. [45]

    High-dimensional quantum key distribution with resource-efficient detection,

    M. Ogrodnik, A. Widomski, D. Bruß,et al., “High-dimensional quantum key distribution with resource-efficient detection,” Opt. Quantum3, 372–380 (2025)

    work page 2025

  46. [46]

    Quantum key distribution with basis-dependent detection probability,

    F. Grasselli, G. Chesi, N. Walk,et al., “Quantum key distribution with basis-dependent detection probability,” Phys. Rev. Appl.23, 044011 (2025)

    work page 2025

  47. [47]

    Experimentalviolationofad-dimensionalbellinequalityusingenergy-time entangled photons,

    S.Schwarz,B.Bessire,andA.Stefanov,“Experimentalviolationofad-dimensionalbellinequalityusingenergy-time entangled photons,” Int. J. Quantum Inf.12, 1560026 (2014)

    work page 2014

  48. [48]

    Phase estimation of time-bin qudits by time-resolved single-photon counting,

    A. Czerwinski, K. Sedziak-Kacprowicz, and P. Kolenderski, “Phase estimation of time-bin qudits by time-resolved single-photon counting,” Phys. Rev. A103, 042402 (2021)

    work page 2021

  49. [49]

    Overcoming noise in entanglement distribution,

    S. Ecker, F. Bouchard, L. Bulla,et al., “Overcoming noise in entanglement distribution,” Phys. Rev. X9, 041042 (2019)

    work page 2019

  50. [50]

    Postselection-Loophole-Free Bell Violation with Genuine Time-Bin Entanglement,

    F. Vedovato, C. Agnesi, M. Tomasin,et al., “Postselection-Loophole-Free Bell Violation with Genuine Time-Bin Entanglement,” Phys. Rev. Lett.121, 190401 (2018)

    work page 2018

  51. [51]

    Post-selectionfreetime-binentanglementonathin-filmlithiumniobate photonic chip,

    M.Bacchi,A.Bernardi, M.Clementi,etal., “Post-selectionfreetime-binentanglementonathin-filmlithiumniobate photonic chip,” arXiv preprint arXiv:2505.04598 (2025)

    work page arXiv 2025

  52. [52]

    Hyperlight | packaged modulators,

    HyperLight Corporation, “Hyperlight | packaged modulators,” (2025). Available at https://hyperlightcorp.com/products/packaged-modulators.php (accessed February 20, 2026)

    work page 2025

  53. [53]

    Low-error encoder for time-bin and decoy states for quantum key distribution,

    D. Scalcon, E. Bazzani, G. Vallone,et al., “Low-error encoder for time-bin and decoy states for quantum key distribution,” npj Quantum Inf.11, 22 (2025)

    work page 2025

  54. [54]

    A Sagnac-based arbitrary time-bin state encoder for quantum communication applications,

    K. Vijayadharan, M. R. Bolaños, M. Avesani,et al., “A Sagnac-based arbitrary time-bin state encoder for quantum communication applications,” EPJ Quantum Technol.12, 129 (2025)

    work page 2025

  55. [55]

    Deterministic unitary operations on time-bin qudits for quantum communication,

    F. Bussières, Y. Soudagar, G. Berlin,et al., “Deterministic unitary operations on time-bin qudits for quantum communication,” arXiv preprint arXiv:quant-ph/0608183 (2006)

    work page arXiv 2006

  56. [56]

    Frequency-encoded photonic qubits for scalable quantum information processing,

    J. M. Lukens and P. Lougovski, “Frequency-encoded photonic qubits for scalable quantum information processing,” Optica4, 8 (2016)

    work page 2016

  57. [57]

    Photon Temporal Modes: A Complete Framework for Quantum Information Science,

    B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon Temporal Modes: A Complete Framework for Quantum Information Science,” Phys. Rev. X5, 041017 (2015)

    work page 2015

  58. [58]

    Integrated frequency comb source of heralded single photons,

    C. Reimer, L. Caspani, M. Clerici,et al., “Integrated frequency comb source of heralded single photons,” Opt. Express22, 6535 (2014)

    work page 2014

  59. [59]

    On-chip generation of high-dimensional entangled quantum states and their coherent control,

    M. Kues, C. Reimer, P. Roztocki,et al., “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature546, 622–626 (2017)

    work page 2017

  60. [60]

    Dissipativekerrsolitonsinopticalmicroresonators,

    T.J.Kippenberg,A.L.Gaeta,M.Lipson,andM.L.Gorodetsky,“Dissipativekerrsolitonsinopticalmicroresonators,” Science361, eaan8083 (2018)

    work page 2018

  61. [61]

    Ramsey interference with single photons,

    S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016)

    work page 2016

  62. [62]

    Characterization of coherent quantum frequency combs using electro-optic phase modulation,

    P. Imany, O. D. Odele, J. A. Jaramillo-Villegas,et al., “Characterization of coherent quantum frequency combs using electro-optic phase modulation,” Phys. Rev. A97, 013813 (2018)

    work page 2018

  63. [63]

    Electro-optic frequency beam splitters and tritters for high-fidelity photonic quantum information processing,

    H.-H. Lu, J. M. Lukens, N. A. Peters,et al., “Electro-optic frequency beam splitters and tritters for high-fidelity photonic quantum information processing,” Phys. Rev. Lett.120, 030502 (2018)

    work page 2018

  64. [64]

    A controlled-not gate for frequency-bin qubits,

    H.-H. Lu, J. M. Lukens, B. P. Williams,et al., “A controlled-not gate for frequency-bin qubits,” npj Quantum Inf.5, 24 (2019)

    work page 2019

  65. [65]

    [’frequency-domain hong–ou–mandel interference’],

    T. Kobayashi, R. Ikuta, S. Yasui,et al., “[’frequency-domain hong–ou–mandel interference’],” Nat. Photon.10, 441–444 (2016)

    work page 2016

  66. [66]

    Frequency-domain hong–ou–mandel interference with linear optics,

    P. Imany, O. D. Odele, M. S. Alshaykh,et al., “Frequency-domain hong–ou–mandel interference with linear optics,” Opt. Lett.43, 2760 (2018)

    work page 2018

  67. [67]

    Quantum interference and correlation control of frequency-bin qubits,

    H.-H. Lu, J. M. Lukens, N. A. Peters,et al., “Quantum interference and correlation control of frequency-bin qubits,” Optica5, 1455 (2018)

    work page 2018

  68. [68]

    Quantum frequency combs and hong–ou–mandel interferometry: the role of spectral phase coherence,

    N. B. Lingaraju, H.-H. Lu, S. Seshadri,et al., “Quantum frequency combs and hong–ou–mandel interferometry: the role of spectral phase coherence,” Opt. Express27, 38683 (2019)

    work page 2019

  69. [69]

    50-ghz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator,

    P. Imany, J. A. Jaramillo-Villegas, O. D. Odele,et al., “50-ghz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator,” Opt. Express26, 1825 (2018)

    work page 2018

  70. [70]

    Generation and coherent control of pulsed quantum frequency combs,

    B. MacLellan, P. Roztocki, M. Kues,et al., “Generation and coherent control of pulsed quantum frequency combs,” J. Vis. Exp. p. 57517 (2018)

    work page 2018

  71. [71]

    High-dimensionalopticalquantumlogicinlargeoperational spaces,

    P.Imany,J.A.Jaramillo-Villegas,M.S.Alshaykh,etal.,“High-dimensionalopticalquantumlogicinlargeoperational spaces,” npj Quantum Inf.5, 59 (2019)

    work page 2019

  72. [72]

    Fully arbitrary control of frequency-bin qubits,

    H.-H. Lu, E. M. Simmerman, P. Lougovski,et al., “Fully arbitrary control of frequency-bin qubits,” Phys. Rev. Lett. 125, 120503 (2020)

    work page 2020

  73. [73]

    Simulations of subatomic many-body physics on a quantum frequency processor,

    H.-H. Lu, N. Klco, J. M. Lukens,et al., “Simulations of subatomic many-body physics on a quantum frequency processor,” Phys. Rev. A100, 012320 (2019)

    work page 2019

  74. [74]

    Quantum phase estimation with time-frequency qudits in a single photon,

    H. Lu, Z. Hu, M. S. Alshaykh,et al., “Quantum phase estimation with time-frequency qudits in a single photon,” Adv. Quantum Technol.3, 1900074 (2019)

    work page 2019

  75. [75]

    Probing quantum walks through coherent control of high- dimensionally entangled photons,

    P. Imany, N. B. Lingaraju, M. S. Alshaykh,et al., “Probing quantum walks through coherent control of high- dimensionally entangled photons,” Sci. Adv.6, eaba8066 (2020)

    work page 2020

  76. [76]

    Programmable frequency-bin quantum states in a nano-engineered silicon device,

    M. Clementi, F. A. Sabattoli, M. Borghi,et al., “Programmable frequency-bin quantum states in a nano-engineered silicon device,” Nat. Commun.14, 176 (2023)

    work page 2023

  77. [77]

    High-dimensional discrete fourier transform gates with a quantum frequency processor,

    H.-H. Lu, N. B. Lingaraju, D. E. Leaird,et al., “High-dimensional discrete fourier transform gates with a quantum frequency processor,” Opt. Express30, 10126 (2022)

    work page 2022

  78. [78]

    Efficient compressive and bayesian characterization of biphoton frequency spectra,

    E. M. Simmerman, H.-H. Lu, A. M. Weiner, and J. M. Lukens, “Efficient compressive and bayesian characterization of biphoton frequency spectra,” Opt. Lett.45, 2886 (2020)

    work page 2020

  79. [79]

    Spectral hong-ou-mandel effect between a heralded single-photon state and a thermal field: Multiphoton contamination and the nonclassicality threshold,

    A. Khodadad Kashi, L. Caspani, and M. Kues, “Spectral hong-ou-mandel effect between a heralded single-photon state and a thermal field: Multiphoton contamination and the nonclassicality threshold,” Phys. Rev. Lett.131, 233601 (2023)

    work page 2023

  80. [80]

    High-dimensional one-way quantum processing implemented on d-level cluster states,

    C. Reimer, S. Sciara, P. Roztocki,et al., “High-dimensional one-way quantum processing implemented on d-level cluster states,” Nat. Phys.15, 148–153 (2018)

    work page 2018

Showing first 80 references.