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 and Joseph M. Lukens ()
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Hsuan-Hao Lu: Quantum Information Science Section, Oak Ridge National Laboratory
Karthik V. Myilswamy: Purdue University
Ryan S. Bennink: Quantum Information Science Section, Oak Ridge National Laboratory
Suparna Seshadri: Purdue University
Mohammed S. Alshaykh: Purdue University
Junqiu Liu: Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL)
Tobias J. Kippenberg: Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL)
Daniel E. Leaird: Purdue University
Andrew M. Weiner: Purdue University
Joseph M. Lukens: Quantum Information Science Section, Oak Ridge National Laboratory

Nature Communications, 2022, vol. 13, issue 1, 1-12

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.

Date: 2022
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DOI: 10.1038/s41467-022-31639-z

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