Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2108.04124 · Nature Communications

Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements

Hsuan‐Hao Lu, Karthik V. Myilswamy, Ryan S. Bennink, Suparna Seshadri, Mohammed S. Alshaykh, Junqiu Liu, Tobias Jan Kippenberg, Daniel E. Leaird, Andrew M. Weiner, Joseph M. Lukens

Published Jul 27, 2022• 81 citations
arXivHTMLPDF

Abstract

Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si3N4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.

DOI
10.1038/s41467-022-31639-z

Related papers

Full quantum state tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements

Hsuan‐Hao Lu, Karthik V. Myilswamy, Ryan S. Bennink +7 more

Abstract Owing in large part to the advent of integrated biphoton frequency combs (BFCs), recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography (QST) of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a novel solution that employs a pulse shaper and electro-optic phase modulator (EOM) to perform random operations instead of mixing in a prescribed manner. Incorporating state-of-the-art Bayesian statistical method, we successfully verify the entanglement and reconstruct the full density matrix of BFCs generated from an on-chip Si3N4 microring resonator (MRR) in up to an 8×8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. Overall, our method furnishes an experimentally powerful approach for frequency-bin tomography with readily implementable operations.

•Aug 30, 2021•1 citation

Randomized tomography of on-chip biphoton frequency combs

Karthik V. Myilswamy, Hsuan‐Hao Lu, Suparna Seshadri +6 more

We perform full state tomography of frequency-bin entangled qudits generated from a Si3N4 microring, up to record-high frequency-bin dimension of d = 8. Our method combines randomized electro-optic modulation and pulse shaping with Bayesian inference.

Frontiers in Optics•Jan 1, 2021•0 citations

Opportunistic full reconstruction of 100-dimensional frequency-bin quantum states

Hanson H. Nguyen, Zachary Goisman, Chen-You Su +5 more

Frequency-bin encoding provides a scalable platform for photonic quantum information processing by enabling high-dimensional qudit states compatible with the telecommunications infrastructure. However, characterizing these systems remains challenging, as conventional quantum state tomography requires measurement resources that increase rapidly with dimensionality, compounded by the difficulty of implementing controllable measurements across many frequency modes at once. Here, we address these challenges and demonstrate threshold quantum state tomography of entangled frequency-bin qudits using adaptive measurements that exploit the sparsity of highly entangled biphoton frequency combs. Combined with Bayesian inference, we experimentally demonstrate full state estimation of biphoton frequency combs with Hilbert space dimensions up to $d^2=100$---a 56% increase over the previous record---all while performing a mere 1.9% of the measurements required by conventional tomographically complete approaches. This work confirms the promise of measurement-aware approaches for characterizing high-dimensional photonic quantum systems, unlocking new tools for full tomography that are hardware-efficient, state-aware, and free from a priori assumptions about state structure.

quant-pharXiv:2610.03496•Oct 5, 2026•0 citations

High-dimensional frequency-bin tomography with random measurements

Hsuan‐Hao Lu, Andrew M. Weiner, Joseph M. Lukens

Utilizing electro-optic modulation and pulse shaping for random measurements, we reconstruct the full density matrix of biphoton frequency combs for entangled qudits up to d = 5. Our method relies on simple experimental settings and can be applied to any frequency-bin quantum system.

Conference on Lasers and Electro-Optics•Jan 1, 2021•0 citations

Toward quantum networking with frequency-bin qudits

Karthik V. Myilswamy, Suparna Seshadri, Hsuan‐Hao Lu +4 more

Quantum networking holds tremendous promise in transforming computation and communication. Entangled-photon sources are critical for quantum repeaters and networking, while photonic integrated circuits are vital for miniaturization and scalability. In this talk, we focus on generating and manipulating frequency-bin entangled states within integrated platforms. We encode quantum information as a coherent superposition of multiple optical frequencies; this approach is favorable due to its amenability to high-dimensional entanglement and compatibility with fiber transmission. We successfully generate and measure the density matrix of biphoton frequency combs from integrated silicon nitride microrings, fully reconstructing the state in an 8 × 8 two-qudit Hilbert space, the highest so far for frequency bins. Moreover, we employ Vernier electro-optic phase modulation methods to perform time-resolved measurements of biphoton correlation functions. Currently, we are exploring bidirectional pumping of microrings to generate indistinguishable entangled pairs in both directions, aiming to demonstrate key networking operations such as entanglement swapping and Greenberger–Horne–Zeilinger state generation in the frequency domain.

Quantum Computing, Communication, and Simulation•Mar 12, 2024•2 citations

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Benjamin MacLellan, Piotr Roztocki, Michael Kues +12 more

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

Journal of Visualized Experiments•Jun 8, 2018•11 citations
Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si3N4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.
Abstract Owing in large part to the advent of integrated biphoton frequency combs (BFCs), recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography (QST) of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a novel solution that employs a pulse shaper and electro-optic phase modulator (EOM) to perform random operations instead of mixing in a prescribed manner. Incorporating state-of-the-art Bayesian statistical method, we successfully verify the entanglement and reconstruct the full density matrix of BFCs generated from an on-chip Si3N4 microring resonator (MRR) in up to an 8×8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. Overall, our method furnishes an experimentally powerful approach for frequency-bin tomography with readily implementable operations.
Frequency-bin encoding provides a scalable platform for photonic quantum information processing by enabling high-dimensional qudit states compatible with the telecommunications infrastructure. However, characterizing these systems remains challenging, as conventional quantum state tomography requires measurement resources that increase rapidly with dimensionality, compounded by the difficulty of implementing controllable measurements across many frequency modes at once. Here, we address these challenges and demonstrate threshold quantum state tomography of entangled frequency-bin qudits using adaptive measurements that exploit the sparsity of highly entangled biphoton frequency combs. Combined with Bayesian inference, we experimentally demonstrate full state estimation of biphoton frequency combs with Hilbert space dimensions up to d2=100d^2=100d2=100---a 56% increase over the previous record---all while performing a mere 1.9% of the measurements required by conventional tomographically complete approaches. This work confirms the promise of measurement-aware approaches for characterizing high-dimensional photonic quantum systems, unlocking new tools for full tomography that are hardware-efficient, state-aware, and free from a priori assumptions about state structure.
Quantum networking holds tremendous promise in transforming computation and communication. Entangled-photon sources are critical for quantum repeaters and networking, while photonic integrated circuits are vital for miniaturization and scalability. In this talk, we focus on generating and manipulating frequency-bin entangled states within integrated platforms. We encode quantum information as a coherent superposition of multiple optical frequencies; this approach is favorable due to its amenability to high-dimensional entanglement and compatibility with fiber transmission. We successfully generate and measure the density matrix of biphoton frequency combs from integrated silicon nitride microrings, fully reconstructing the state in an 8 × 8 two-qudit Hilbert space, the highest so far for frequency bins. Moreover, we employ Vernier electro-optic phase modulation methods to perform time-resolved measurements of biphoton correlation functions. Currently, we are exploring bidirectional pumping of microrings to generate indistinguishable entangled pairs in both directions, aiming to demonstrate key networking operations such as entanglement swapping and Greenberger–Horne–Zeilinger state generation in the frequency domain.
We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.