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 J. Kippenberg; Daniel E. Leaird; Andrew M. Weiner; Joseph M. Lukens

doi:10.1038/s41467-022-31639-z

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 J. Kippenberg, Daniel E. Leaird, Andrew M. Weiner, Joseph M. Lukens

Research output: Contribution to journal › Article › peer-review

52 Scopus 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.

Original language	English
Article number	4338
Journal	Nature Communications
Volume	13
Issue number	1
DOIs	https://doi.org/10.1038/s41467-022-31639-z
State	Published - Dec 2022

Funding

We thank AdvR for loaning the PPLN ridge waveguide; P. Imany, N.B. Lingaraju, and A.J. Moore for valuable discussions; A.A.N. Ovi for laboratory help; and B.T. Kirby for introducing us to the Bures distribution. This work was performed in part at Oak Ridge National Laboratory, operated by UT-Battelle for the U.S. Department of Energy under contract no. DE-AC05-00OR22725. Funding was provided by the U.S. Department of Energy, Office of Advanced Scientific Computing Research, Early Career Research Program (Field Work Proposal ERKJ353), the National Science Foundation (1839191-ECCS, 2034019-ECCS), the Air Force Office of Scientific Research (Award no. FA9550-19-1-0250), and the Swiss National Science Foundation under Grant no. 176563 (BRIDGE). K.V.M. acknowledges support from the QISE-NET fellowship program of the National Science Foundation (DMR-1747426). M.S.A. acknowledges support from the College of Engineering Research Center at King Saud University. The Si3 N4 samples were fabricated in the EPFL Center of MicroNanoTechnology (CMi). We thank AdvR for loaning the PPLN ridge waveguide; P. Imany, N.B. Lingaraju, and A.J. Moore for valuable discussions; A.A.N. Ovi for laboratory help; and B.T. Kirby for introducing us to the Bures distribution. This work was performed in part at Oak Ridge National Laboratory, operated by UT-Battelle for the U.S. Department of Energy under contract no. DE-AC05-00OR22725. Funding was provided by the U.S. Department of Energy, Office of Advanced Scientific Computing Research, Early Career Research Program (Field Work Proposal ERKJ353), the National Science Foundation (1839191-ECCS, 2034019-ECCS), the Air Force Office of Scientific Research (Award no. FA9550-19-1-0250), and the Swiss National Science Foundation under Grant no. 176563 (BRIDGE). K.V.M. acknowledges support from the QISE-NET fellowship program of the National Science Foundation (DMR-1747426). M.S.A. acknowledges support from the College of Engineering Research Center at King Saud University. The SiN samples were fabricated in the EPFL Center of MicroNanoTechnology (CMi). 3 4

Funders	Funder number
College of Engineering Research Center at King Saud University
EPFL Center of MicroNanoTechnology
QISE-NET	DMR-1747426
National Science Foundation	1839191-ECCS, 2034019-ECCS
U.S. Department of Energy	DE-AC05-00OR22725
Air Force Office of Scientific Research	FA9550-19-1-0250
Advanced Scientific Computing Research	ERKJ353
Oak Ridge National Laboratory
UT-Battelle
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung	176563

Access to Document

10.1038/s41467-022-31639-z

Cite this

@article{010a2849abb443f796b424287a1ca003,

title = "Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements",

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.",

author = "Lu, {Hsuan Hao} and Myilswamy, {Karthik V.} and Bennink, {Ryan S.} and Suparna Seshadri and Alshaykh, {Mohammed S.} and Junqiu Liu and Kippenberg, {Tobias J.} and Leaird, {Daniel E.} and Weiner, {Andrew M.} and Lukens, {Joseph M.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = dec,

doi = "10.1038/s41467-022-31639-z",

language = "English",

volume = "13",

journal = "Nature Communications",

issn = "2041-1723",

publisher = "Nature Research",

number = "1",

}

TY - JOUR

T1 - Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements

AU - Lu, Hsuan Hao

AU - Myilswamy, Karthik V.

AU - Bennink, Ryan S.

AU - Seshadri, Suparna

AU - Alshaykh, Mohammed S.

AU - Liu, Junqiu

AU - Kippenberg, Tobias J.

AU - Leaird, Daniel E.

AU - Weiner, Andrew M.

AU - Lukens, Joseph M.

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85135020794&partnerID=8YFLogxK

U2 - 10.1038/s41467-022-31639-z

DO - 10.1038/s41467-022-31639-z

M3 - Article

C2 - 35896534

AN - SCOPUS:85135020794

SN - 2041-1723

VL - 13

JO - Nature Communications

JF - Nature Communications

IS - 1

M1 - 4338

ER -

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

Abstract

Funding

Access to Document

Other files and links

Fingerprint

Cite this