High-Dimensional Pixel Entanglement: Efficient Generation and Certification

Natalia Herrera Valencia1, Vatshal Srivastav1, Matej Pivoluska2,3, Marcus Huber4,5, Nicolai Friis4, Will McCutcheon1, and Mehul Malik1,4

1Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, UK
2Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
3Institute of Computer Science, Masaryk University, Brno, Czech Republic
4Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Vienna, Austria
5Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria

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Abstract

Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.

Entanglement has been demonstrated using many different properties of light, such as its polarisation, path, or spatial and temporal structure. The inherently high-dimensional nature of the photonic wavefunction enables one to explore entanglement significantly beyond the qubit regime, which offers several advantages in terms of information capacity and noise-robustness. However, the generation and measurement of such large quantum-entangled states is often challenging, limited by the quality, ease, scalability, and speed of generalised measurements in space and time. Here we demonstrate high-dimensional entanglement of two photons in their localised transverse spatial position or “pixel” modes. Through the use of carefully engineered measurements and a specially designed entanglement witness, we certify high-dimensional pixel entanglement with a record dimensionality, quality, and measurement speed. Some examples of our measured states include entanglement in 55 local dimensions, state fidelities of up to 98.2%, and 100-fold improvements in measurement times. Our work has the potential to significantly advance quantum communication systems by pushing their capacity limits and resilience to noise.

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[29] Carlos Sevilla-Gutiérrez, Varun Raj Kaipalath, Baghdasar Baghdasaryan, Markus Gräfe, Stephan Fritzsche, and Fabian Steinlechner, "Spectral properties of transverse Laguerre-Gauss modes in parametric down-conversion", Physical Review A 109 2, 023534 (2024).

[30] Mirdit Doda, Marcus Huber, Gláucia Murta, Matej Pivoluska, Martin Plesch, and Chrysoula Vlachou, "Quantum Key Distribution Overcoming Extreme Noise: Simultaneous Subspace Coding Using High-Dimensional Entanglement", Physical Review Applied 15 3, 034003 (2021).

[31] Vatshal Srivastav, Natalia Herrera Valencia, Saroch Leedumrongwatthanakun, Will McCutcheon, and Mehul Malik, "Characterizing and Tailoring Spatial Correlations in Multimode Parametric Down-Conversion", Physical Review Applied 18 5, 054006 (2022).

[32] Sergei Slussarenko, Dominick J. Joch, Nora Tischler, Farzad Ghafari, Lynden K. Shalm, Varun B. Verma, Sae Woo Nam, and Geoff J. Pryde, "Quantum steering with vector vortex photon states with the detection loophole closed", npj Quantum Information 8 1, 20 (2022).

[33] Sebastian Ecker, Philipp Sohr, Lukas Bulla, Rupert Ursin, and Martin Bohmann, "Remotely Establishing Polarization Entanglement Over Noisy Polarization Channels", Physical Review Applied 17 3, 034009 (2022).

[34] Bereneice Sephton, Isaac Nape, Chané Moodley, Jason Francis, and Andrew Forbes, "Revealing the embedded phase in single-pixel quantum ghost imaging", Optica 10 2, 286 (2023).

[35] Julius Arthur Bittermann, Lukas Bulla, Sebastian Ecker, Sebastian Philipp Neumann, Matthias Fink, Martin Bohmann, Nicolai Friis, Marcus Huber, and Rupert Ursin, "Photonic entanglement during a zero-g flight", Quantum 8, 1256 (2024).

[36] Zhen-Peng Xu, Jonathan Steinberg, Jaskaran Singh, Antonio J. López-Tarrida, José R. Portillo, and Adán Cabello, "Graph-theoretic approach to Bell experiments with low detection efficiency", Quantum 7, 922 (2023).

[37] Baptiste Courme, Chloé Vernière, Peter Svihra, Sylvain Gigan, Andrei Nomerotski, and Hugo Defienne, "Quantifying high-dimensional spatial entanglement with a single-photon-sensitive time-stamping camera", Optics Letters 48 13, 3439 (2023).

[38] Ohad Lib and Yaron Bromberg, "Thermal biphotons", APL Photonics 7 3, 031301 (2022).

[39] Suraj Goel, Saroch Leedumrongwatthanakun, Natalia Herrera Valencia, Will McCutcheon, Armin Tavakoli, Claudio Conti, Pepijn W. H. Pinkse, and Mehul Malik, "Inverse design of high-dimensional quantum optical circuits in a complex medium", Nature Physics 20 2, 232 (2024).

[40] Vatshal Srivastav, Natalia Herrera Valencia, Will McCutcheon, Saroch Leedumrongwatthanakun, Sébastien Designolle, Roope Uola, Nicolas Brunner, and Mehul Malik, "Quick Quantum Steering: Overcoming Loss and Noise with Qudits", Physical Review X 12 4, 041023 (2022).

[41] Isaac Nape, Bereneice Sephton, Pedro Ornelas, Chane Moodley, and Andrew Forbes, "Quantum structured light in high dimensions", APL Photonics 8 5, 051101 (2023).

[42] Vatshal Srivastav, Natalia Herrera Valencia, Will McCutcheon, Saroch Leedumrongwatthanakun, Sébastien Designolle, Roope Uola, Nicolas Brunner, and Mehul Malik, Quantum 2.0 Conference and Exhibition QTu3B.4 (2022) ISBN:978-1-957171-11-1.

[43] Vatshal Srivastav, Natalia Herrera Valencia, Will McCutcheon, Saroch Leedumrongwatthanakun, Sébastien Designolle, Roope Uola, Nicolas Brunner, and Mehul Malik, CLEO 2023 FM1A.1 (2023) ISBN:978-1-957171-25-8.

[44] Lukas Bulla, Kristian Hjorth, Oskar Kohout, Jan Lang, Sebastian Ecker, Sebastian P. Neumann, Julius Bittermann, Robert Kindler, Marcus Huber, Martin Bohmann, Rupert Ursin, and Matej Pivoluska, "Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere", Physical Review A 107 5, L050402 (2023).

[45] Oliver F. Thomas, Will McCutcheon, and Dara P. S. McCutcheon, "A general framework for multimode Gaussian quantum optics and photo-detection: Application to Hong–Ou–Mandel interference with filtered heralded single photon sources", APL Photonics 6 4, 040801 (2021).

[46] Zhi-Feng Liu, Chao Chen, Jia-Min Xu, Zi-Mo Cheng, Zhi-Cheng Ren, Bo-Wen Dong, Yan-Chao Lou, Yu-Xiang Yang, Shu-Tian Xue, Zhi-Hong Liu, Wen-Zheng Zhu, Xi-Lin Wang, and Hui-Tian Wang, "Hong-Ou-Mandel Interference between Two Hyperentangled Photons Enables Observation of Symmetric and Antisymmetric Particle Exchange Phases", Physical Review Letters 129 26, 263602 (2022).

[47] Matteo Fadel, Quantum Science and Technology 57 (2021) ISBN:978-3-030-85471-3.

[48] Xiao-Min Hu, Chao Zhang, Bi-Heng Liu, Yu Cai, Xiang-Jun Ye, Yu Guo, Wen-Bo Xing, Cen-Xiao Huang, Yun-Feng Huang, Chuan-Feng Li, and Guang-Can Guo, "Experimental High-Dimensional Quantum Teleportation", Physical Review Letters 125 23, 230501 (2020).

[49] Xiao-Min Hu, Wen-Bo Xing, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Paul Erker, and Marcus Huber, "Efficient Generation of High-Dimensional Entanglement through Multipath Down-Conversion", Physical Review Letters 125 9, 090503 (2020).

[50] Natalia Herrera Valencia, Suraj Goel, Will McCutcheon, Hugo Defienne, and Mehul Malik, "Unscrambling entanglement through a complex medium", Nature Physics 16 11, 1112 (2020).

[51] Bienvenu Ndagano, Hugo Defienne, Ashley Lyons, Ilya Starshynov, Federica Villa, Simone Tisa, and Daniele Faccio, "Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera", npj Quantum Information 6, 94 (2020).

[52] Feng Zhu, Max Tyler, Natalia Herrera Valencia, Mehul Malik, and Jonathan Leach, "Is high-dimensional photonic entanglement robust to noise?", arXiv:1908.08943, (2019).

[53] Suraj Goel, Matthew Reynolds, Matthew Girling, Will McCutcheon, Saroch Leedumrongwatthanakun, Vatshal Srivastav, David Jennings, Mehul Malik, and Jiannis K. Pachos, "Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation", arXiv:2304.05286, (2023).

[54] Xiao-Min Hu, Wen-Bo Xing, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Guang-Can Guo, Paul Erker, and Marcus Huber, "Efficient generation of high-dimensional entanglement through multi-path downconversion", arXiv:2004.09964, (2020).

[55] Natalia Herrera Valencia, Vatshal Srivastav, Saroch Leedumrongwatthanakun, Will McCutcheon, and Mehul Malik, "Entangled ripples and twists of light: Radial and azimuthal Laguerre-Gaussian mode entanglement", arXiv:2104.04506, (2021).

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