Abstract
We present an entanglement-based quantitative phase gradient microscopy technique that employs principles from quantum ghost imaging and ghost diffraction. In this method, a transparent sample is illuminated by both photons of an entangled pair–one detected in the near-field (position) and the other in the far-field (momentum). Due to the strong correlations offered by position-momentum entanglement, both conjugate observables can be inferred nonlocally, effectively enabling simultaneous access to the sample’s transmission and phase gradient information. This dual-domain measurement allows for the quantitative recovery of the full amplitude and phase profile of the sample. Unlike conventional classical and quantum phase imaging methods, our approach requires no interferometry, spatial scanning, microlens arrays, or iterative phase-retrieval algorithms, thereby circumventing many of their associated limitations. Furthermore, intrinsic temporal correlations between entangled photons provide robustness against dynamic and structured background light. We demonstrate quantitative phase and amplitude imaging with a spatial resolution of 2.76 μm and a phase sensitivity of λ/100 using femtowatts of illuminating power. This technique opens new possibilities for non-invasive imaging of photosensitive samples, wavefront sensing in adaptive optics, and imaging under complex lighting environments.
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Data availability
The raw data generated in this study are available from the corresponding authors upon request. Due to the large data size, public deposition is not feasible.
Code availability
The code for phase recovery from coincidence data and a sample dataset is available on Zenodo64.
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Acknowledgements
This work was supported by NRC-uOttawa Joint Centre for Extreme Quantum Photonics (JCEP) via the Quantum Sensors Challenge Program at the National Research Council of Canada (E.K., B.S.), Quantum Enhanced Sensing and Imaging (QuEnSI) Alliance Consortia Quantum grant (E.K., B.S.), the Canada Research Chair (CRC) Program (E.K.) and from the Ministry of Education (MOE), Taiwan, under the Yushan Fellow Program (P.-A.M.), and from the National Science and Technology Council (NSTC), Taiwan (114-2112-M-006-023 P.-A.M.).
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Y.Z. performed the experiment and conducted the data analysis. Y.Z., P.-A.M. and D.E. conceived the idea. E.K. and B.S. secured the funding and supervised the project. All authors contributed to writing the manuscript.
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Zhang, Y., Moreau, PA., England, D. et al. Quantitative phase gradient microscopy with spatially entangled photons. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69881-4
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DOI: https://doi.org/10.1038/s41467-026-69881-4
