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

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


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.

► BibTeX data

► References

[1] Charles H. Bennett, Peter W. Shor, John A. Smolin, and Ashish V. Thapliyal, Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem, IEEE T. Inform. Theory 48, 2637 (2002), arXiv:quant-ph/​0106052.

[2] Umesh Vazirani and Thomas Vidick, Fully Device-Independent Quantum Key Distribution, Phys. Rev. Lett. 113, 140501 (2014), arXiv:1210.1810.

[3] Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani, Device-Independent Security of Quantum Cryptography against Collective Attacks, Phys. Rev. Lett. 98, 230501 (2007), arXiv:quant-ph/​0702152.

[4] Marissa Giustina, Marijn A. M. Versteegh, Sören Wengerowsky, Johannes Handsteiner, Armin Hochrainer, Kevin Phelan, Fabian Steinlechner, Johannes Kofler, Jan-Åke Larsson, Carlos Abellán, Waldimar Amaya, Valerio Pruneri, Morgan W. Mitchell, Jörn Beyer, Thomas Gerrits, Adriana E. Lita, Lynden K. Shalm, Sae Woo Nam, Thomas Scheidl, Rupert Ursin, Bernhard Wittmann, and Anton Zeilinger, Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons, Phys. Rev. Lett. 115, 250401 (2015), arXiv:1511.03190.

[5] Lynden K Shalm, Evan Meyer-Scott, Bradley G Christensen, Peter Bierhorst, Michael A Wayne, Martin J Stevens, Thomas Gerrits, Scott Glancy, Deny R Hamel, Michael S Allman, Kevin J Coakley, Shellee D Dyer, Carson Hodge, Adriana E Lita, Varun B Verma, Camilla Lambrocco, Edward Tortorici, Alan L Migdall, Yanbao Zhang, Daniel R Kumor, William H Farr, Francesco Marsili, Matthew D Shaw, Jeffrey A Stern, Carlos Abellán, Waldimar Amaya, Valerio Pruneri, Thomas Jennewein, Morgan W Mitchell, Paul G Kwiat, Joshua C Bienfang, Richard P Mirin, Emanuel Knill, and Sae Woo Nam, Strong Loophole-Free Test of Local Realism, Phys. Rev. Lett. 115, 250402 (2015), arxiv:1511.03189.

[6] Massimiliano Proietti, Alexander Pickston, Francesco Graffitti, Peter Barrow, Dmytro Kundys, Cyril Branciard, Martin Ringbauer, and Alessandro Fedrizzi, Experimental test of local observer independence, Sci. Adv. 5, eaaw9832 (2019), arXiv:1902.05080.

[7] Nurul T Islam, Charles Ci Wen Lim, Clinton Cahall, Jungsang Kim, and Daniel J Gauthier, Provably secure and high-rate quantum key distribution with time-bin qudits, Sci. Adv. 3, e1701491 (2017), arXiv:1709.06135.

[8] Mohammad Mirhosseini, Omar S Magaña-Loaiza, Malcolm N O'Sullivan, Brandon Rodenburg, Mehul Malik, Martin P J Lavery, Miles J Padgett, Daniel J Gauthier, and Robert W Boyd, High-dimensional quantum cryptography with twisted light, New J. Phys. 17, 33033 (2015), arXiv:1402.7113.

[9] Sebastian Ecker, Frédéric Bouchard, Lukas Bulla, Florian Brandt, Oskar Kohout, Fabian Steinlechner, Robert Fickler, Mehul Malik, Yelena Guryanova, Rupert Ursin, and Marcus Huber, Overcoming Noise in Entanglement Distribution, Phys. Rev. X 9, 041042 (2019), arXiv:1904.01552.

[10] Feng Zhu, Max Tyler, Natalia Herrera Valencia, Mehul Malik, and Jonathan Leach, Are high-dimensional entangled states robust to noise? (2019), arXiv:1908.08943.

[11] Alexia Salavrakos, Remigiusz Augusiak, Jordi Tura, Peter Wittek, Antonio Acín, and Stefano Pironio, Bell Inequalities Tailored to Maximally Entangled States, Phys. Rev. Lett. 119, 040402 (2017), arXiv:1607.04578.

[12] Tamás Vertesi, Stefano Pironio, and Nicolas Brunner, Closing the Detection Loophole in Bell Experiments Using Qudits, Phys. Rev. Lett. 104, 60401 (2010), arXiv:0909.3171.

[13] Pranav Gokhale, Jonathan M. Baker, Casey Duckering, Natalie C. Brown, Kenneth R. Brown, and Frederic T. Chong, Asymptotic Improvements to Quantum Circuits via Qutrits, Proc. Int. Symp. Comput. Archit. , 554 (2019), arXiv:1905.10481.

[14] Nicolai Friis, Giuseppe Vitagliano, Mehul Malik, and Marcus Huber, Entanglement Certification From Theory to Experiment, Nat. Rev. Phys. 1, 72 (2019), arXiv:1906.10929.

[15] Megan Agnew, Jonathan Leach, Melanie McLaren, F Stef Roux, and Robert W Boyd, Tomography of the quantum state of photons entangled in high dimensions, Phys. Rev. A 84, 062101 (2011), arXiv:1905.10481.

[16] Anthony Martin, Thiago Guerreiro, Alexey Tiranov, Sébastien Designolle, Florian Fröwis, Nicolas Brunner, Marcus Huber, and Nicolas Gisin, Quantifying Photonic High-Dimensional Entanglement, Phys. Rev. Lett. 118, 110501 (2017), arXiv:1701.03269.

[17] Alexey Tiranov, Sébastien Designolle, Emmanuel Zambrini Cruzeiro, Jonathan Lavoie, Nicolas Brunner, Mikael Afzelius, Marcus Huber, and Nicolas Gisin, Quantification of multidimensional entanglement stored in a crystal, Phys. Rev. A 96, 040303 (2017), arXiv:1609.05033.

[18] James Schneeloch, Christopher C Tison, Michael L Fanto, Paul M Alsing, and Gregory A Howland, Quantifying entanglement in a 68-billion-dimensional quantum state space, Nat. Commun. 10, 2785 (2019), arXiv:1804.04515.

[19] Michael Kues, Christian Reimer, Piotr Roztocki, Luis Romero Cortés, Stefania Sciara, Benjamin Wetzel, Yanbing Zhang, Alfonso Cino, Sai T Chu, Brent E Little, David J Moss, Lucia Caspani, José Azaña, and Roberto Morandotti, On-chip generation of high-dimensional entangled quantum states and their coherent control, Nature 546, 622 (2017).

[20] Mario Krenn, Marcus Huber, Robert Fickler, Radek Lapkiewicz, Sven Ramelow, and Anton Zeilinger, Generation and confirmation of a $(100\times100)$-dimensional entangled quantum system, Proc. Natl. Acad. Sci. U.S.A. 111, 6243 (2014), arXiv:1306.0096.

[21] P Erker, M Krenn, and Marcus Huber, Quantifying high dimensional entanglement with two mutually unbiased bases, Quantum 1, 22 (2017), arxiv:1512.05315.

[22] Jessica Bavaresco, Natalia Herrera Valencia, Claude Klöckl, Matej Pivoluska, Paul Erker, Nicolai Friis, Mehul Malik, and Marcus Huber, Measurements in two bases are sufficient for certifying high-dimensional entanglement, Nat. Phys. 14, 1032 (2018), arXiv:1709.07344.

[23] Adetunmise C Dada, Jonathan Leach, Gerald S Buller, Miles J Padgett, and Erika Andersson, Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities, Nat. Phys. 7, 677 (2011), arXiv:1104.5087.

[24] Jianwei Wang, Stefano Paesani, Yunhong Ding, Raffaele Santagati, Paul Skrzypczyk, Alexia Salavrakos, Jordi Tura, Remigiusz Augusiak, Laura Mančinska, Davide Bacco, Damien Bonneau, Joshua W Silverstone, Qihuang Gong, Antonio Acín, Karsten Rottwitt, Leif K Oxenløwe, Jeremy L O'Brien, Anthony Laing, and Mark G Thompson, Multidimensional quantum entanglement with large-scale integrated optics, Science 360, 285 (2018), arXiv:1803.04449.

[25] Fulvio Flamini, Nicolò Spagnolo, Niko Viggianiello, Andrea Crespi, Roberto Osellame, and Fabio Sciarrino, Benchmarking integrated linear-optical architectures for quantum information processing, Sci. Rep. 7, 1 (2017), arXiv:1705.09211.

[26] Mario Krenn, Mehul Malik, Manuel Erhard, and Anton Zeillinger, Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes, Philos. T. R. Soc. A 375, 20150442 (2017), arXiv:1607.05114.

[27] Manuel Erhard, Mehul Malik, Mario Krenn, and Anton Zeilinger, Experimental Greenberger-Horne-Zeilinger entanglement beyond qubits, Nat. Phot. 12, 759 (2018), arXiv:1708.03881.

[28] Victor Arrizon, Ulises Ruiz, Rosibel Carrada, and Luis A Gonzalez, Pixelated phase computer holograms for the accurate encoding of scalar complex fields, J. Opt. Soc. Am. A 24, 3500 (2007).

[29] Frédéric Bouchard, Natalia Herrera Valencia, Florian Brandt, Robert Fickler, Marcus Huber, and Mehul Malik, Measuring azimuthal and radial modes of photons, Opt. Express 26, 31925 (2018), arXiv:1808.03533.

[30] Hammam Qassim, Filippo M Miatto, Juan P Torres, Miles J Padgett, Ebrahim Karimi, and Robert W Boyd, Limitations to the determination of a Laguerre-Gauss spectrum via projective, phase-flattening measurement, J. Opt. Soc. Am. B 31, A20 (2014), arXiv:1401.3512.

[31] Malcolm N. O'Sullivan-Hale, Irfan Ali Khan, Robert W Boyd, and John C. Howell, Pixel Entanglement: Experimental Realization of Optically Entangled d=3 and d=6 Qudits, Phys. Rev. Lett. 94, 220501 (2005).

[32] M P Edgar, D S Tasca, F Izdebski, R E Warburton, J Leach, M Agnew, G S Buller, R W Boyd, and Miles J Padgett, Imaging high-dimensional spatial entanglement with a camera, Nat. Commun. 3, 984 (2012), arXiv:1204.1293.

[33] James Schneeloch and John C Howell, Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone, J. Opt. 18, 53501 (2016), arXiv:1502.06996.

[34] F M Miatto, H Di Lorenzo Pires, S M Barnett, and M P van Exter, Spatial Schmidt modes generated in parametric down-conversion, Eur. Phys. J. D 66, 263 (2012), arXiv:1201.3041.

[35] E. V. Kovlakov, S. S. Straupe, and S. P. Kulik, Quantum state engineering with twisted photons via adaptive shaping of the pump beam, Phys. Rev. A 98, 060301 (2018), arXiv:1807.09804.

[36] Shilong Liu, Zhiyuan Zhou, Shikai Liu, Yinhai Li, Yan Li, Chen Yang, Zhaohuai Xu, Zhaodi Liu, Guangcan Guo, and Baosen Shi, Coherent manipulation of a three-dimensional maximally entangled state, Phys. Rev. A 98, 062316 (2018), arXiv:1807.07257.

[37] J. Cariñe, G. Cañas, P. Skrzypczyk, I. Šupić, N. Guerrero, T. Garcia, L. Pereira, M. A. S. Prosser, G. B. Xavier, A. Delgado, S. P. Walborn, D. Cavalcanti, and G. Lima, Multi-core fiber integrated multi-port beam splitters for quantum information processing, Optica 7, 542 (2020), arXiv:2001.11056.

[38] Beatrice Da Lio, Leif Katsuo Oxenlowe, Davide Bacco, Daniele Cozzolino, Nicola Biagi, Tummas Napoleon Arge, Emil Larsen, Karsten Rottwitt, Yunhong Ding, and Alessandro Zavatta, Stable Transmission of High-Dimensional Quantum States Over a 2-km Multicore Fiber, IEEE J. Sel. Top. Quantum Electron. 26, 1 (2020), arXiv:2001.11056.

[39] Hee Jung Lee and Hee Su Park, Generation and measurement of arbitrary four-dimensional spatial entanglement between photons in multicore fibers, Photon. Res 7, 19 (2019).

[40] E.S Gómez, S. Gómez, I. Machuca, A. Cabello, S. Pádua, S.P. Walborn, and G. Lima, Multi-dimensional entanglement generation with multi-core optical fibers, (2020), arXiv:2005.07847.

[41] Natalia Herrera Valencia, Suraj Goel, Will McCutcheon, Hugo Defienne, and Mehul Malik, Unscrambling entanglement through a complex medium, Nat, Phys. 16, 1112–1116 (2020), arXiv:1910.04490.

[42] Sébastien Designolle, Vatshal Srivastav, Roope Uola, Natalia Herrera Valencia, Will McCutcheon, Mehul Malik, and Nicolas Brunner, Genuine high-dimensional quantum steering, (2020), arXiv:2007.02718.

[43] Alipasha Vaziri, Jian-Wei Pan, Thomas Jennewein, Gregor Weihs, and Anton Zeilinger, Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum, Phys. Rev. Lett. 91, 227902 (2003), arXiv:quant-ph/​0303003.

[44] W.K. Wootters and B.D. Fields, Optimal state-determination by mutually unbiased measurements, Ann. Phys. (N. Y). 191, 363 (1989).

[45] Armin Tavakoli, Máté Farkas, Denis Rosset, Jean-Daniel Bancal, and Jȩdrzej Kaniewski, Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments: Bell inequalities, device-independent certification and applications, (2019), arXiv:1912.03225.

[46] Flavien Hirsch and Marcus Huber, The Schmidt number of a quantum state cannot always be device-independently certified, (2020), arXiv:2003.14189.

[47] William K. Wootters, Entanglement of formation and concurrence, Quantum Inf. Comput. 1, 27 (2001).

[48] Patrick J. Coles, Mario Berta, Marco Tomamichel, and Stephanie Wehner, Entropic uncertainty relations and their applications, Rev. Mod. Phys. 89, 015002 (2017), arxiv:1511.04857.

[49] Xiao-Min Hu, Wen-Bo Xing, Bi-Heng Liu, Yun-Feng Huang, Paul Erker, Marcus Huber, Chuan-Feng Li, and Guang-Can Guo, Efficient Generation of High-Dimensional Entanglement through Multipath Down-Conversion, Phys. Rev. Lett. 125, 090503 (2020), arXiv:2004.09964.

[50] Mohammad Mirhosseini, Mehul Malik, Zhimin Shi, and Robert W Boyd, Efficient separation of the orbital angular momentum eigenstates of light, Nat. Commun. 4, 2781 (2013), arXiv:1306.0849.

[51] Nicolas K Fontaine, Roland Ryf, Haoshuo Chen, David T Neilson, Kwangwoong Kim, and Joel Carpenter, Laguerre-Gaussian mode sorter, Nat. Commun. 10, 1865 (2019), arXiv:1803.04126.

[52] Florian Brandt, Markus Hiekkamäki, Frédéric Bouchard, Marcus Huber, and Robert Fickler, High-dimensional quantum gates using full-field spatial modes of photons, Optica 7, 98 (2020), arXiv:1907.13002.

[53] Emma E. Wollman, Varun B. Verma, Adriana E. Lita, William H. Farr, Matthew D. Shaw, Richard P. Mirin, and Sae Woo Nam, Kilopixel array of superconducting nanowire single-photon detectors, Opt. Express 27, 35279 (2019), arXiv:1908.10520.

Cited by

[1] Joonwoo Bae, Anindita Bera, Dariusz Chruściński, Beatrix C Hiesmayr, and Daniel McNulty, "How many mutually unbiased bases are needed to detect bound entangled states?", Journal of Physics A: Mathematical and Theoretical 55 50, 505303 (2022).

[2] Cade Peters, Pedro Ornelas, Isaac Nape, and Andrew Forbes, "Spatially resolving classical and quantum entanglement with structured photons", Physical Review A 108 5, 053502 (2023).

[3] Suraj Goel, Saroch Leedumrongwatthanakun, Natalia Herrera Valencia, Will McCutcheon, Armin Tavakoli, Claudio Conti, Pepijn W. H. Pinkse, and Mehul Malik, Frontiers in Optics + Laser Science 2023 (FiO, LS) FM6B.7 (2023) ISBN:978-1-957171-29-6.

[4] Ohad Lib, Kfir Sulimany, and Yaron Bromberg, "Processing Entangled Photons in High Dimensions with a Programmable Light Converter", Physical Review Applied 18 1, 014063 (2022).

[5] Hui Zhang, Lingxiao Wan, Tobias Haug, Wai-Keong Mok, Stefano Paesani, Yuzhi Shi, Hong Cai, Lip Ket Chin, Muhammad Faeyz Karim, Limin Xiao, Xianshu Luo, Feng Gao, Bin Dong, Syed Assad, M. S. Kim, Anthony Laing, Leong Chuan Kwek, and Ai Qun Liu, "Resource-efficient high-dimensional subspace teleportation with a quantum autoencoder", Science Advances 8 40, eabn9783 (2022).

[6] Simon Morelli, David Sauerwein, Michalis Skotiniotis, and Nicolai Friis, "Metrology-assisted entanglement distribution in noisy quantum networks", Quantum 6, 722 (2022).

[7] Andrew Forbes, Mostafa Youssef, Sachleen Singh, Isaac Nape, and Bora Ung, "Quantum cryptography with structured photons", Applied Physics Letters 124 11, 110501 (2024).

[8] Simon Morelli, Hayata Yamasaki, Marcus Huber, and Armin Tavakoli, "Entanglement Detection with Imprecise Measurements", Physical Review Letters 128 25, 250501 (2022).

[9] Junior R. Gonzales-Ureta, Ana Predojević, and Adán Cabello, "Optimal and tight Bell inequalities for state-independent contextuality sets", Physical Review Research 5 1, L012035 (2023).

[10] 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(S3) Anyons Using a Classical Photonic Simulator", Physical Review Letters 132 11, 110601 (2024).

[11] Simon Morelli, Marcus Huber, and Armin Tavakoli, "Resource-Efficient High-Dimensional Entanglement Detection via Symmetric Projections", Physical Review Letters 131 17, 170201 (2023).

[12] Alessio D’Errico, Felix Hufnagel, Filippo Miatto, Mohammadreza Rezaee, and Ebrahim Karimi, "Full-mode characterization of correlated photon pairs generated in spontaneous downconversion", Optics Letters 46 10, 2388 (2021).

[13] Yan-Han Yang, Xue Yang, and Ming-Xing Luo, "Detecting and embedding high-dimensional genuine multipartite entanglement states", Quantum Information Processing 21 11, 364 (2022).

[14] Zheshen Zhang, Chenglong You, Omar S. Magaña-Loaiza, Robert Fickler, Roberto de J. León-Montiel, Juan P. Torres, Travis S. Humble, Shuai Liu, Yi Xia, and Quntao Zhuang, "Entanglement-based quantum information technology: a tutorial", Advances in Optics and Photonics 16 1, 60 (2024).

[15] 晓旭 罗, "Entanglement Detection Considering Experimental Inaccuracies", Advances in Applied Mathematics 13 05, 2180 (2024).

[16] 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).

[17] 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).

[18] 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).

[19] 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).

[20] 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).

[21] 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).

[22] 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.

[23] 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.

[24] 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).

[25] 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).

[26] 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 ", Journal of Optics 23 10, 104001 (2021).

[27] Bereneice Sephton, Adam Vallés, Isaac Nape, Mitchell A. Cox, Fabian Steinlechner, Thomas Konrad, Juan P. Torres, Filippus S. Roux, and Andrew Forbes, "Quantum transport of high-dimensional spatial information with a nonlinear detector", Nature Communications 14 1, 8243 (2023).

[28] Dylan Danese, Sabine Wollmann, Saroch Leedumrongwatthanakun, Will McCutcheon, Manuel Erhard, William N. Plick, and Mehul Malik, " ℓ 00 ℓ entanglement and the twisted quantum eraser", AVS Quantum Science 5 4, 045004 (2023).

[29] Qiang Zeng, Jiangwei Shang, H. Chau Nguyen, and Xiangdong Zhang, "Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering", Physical Review Research 4 1, 013151 (2022).

[30] Zhihe Zhang, Dongkai Zhang, Xiaodong Qiu, Yuanyuan Chen, Sonja Franke-Arnold, and Lixiang Chen, "Experimental investigation of the uncertainty principle for radial degrees of freedom", Photonics Research 10 9, 2223 (2022).

[31] F. Zhu, M. Tyler, N. H. Valencia, M. Malik, and J. Leach, "Is high-dimensional photonic entanglement robust to noise?", AVS Quantum Science 3 1, 011401 (2021).

[32] Xiaoqin Gao, Paul Appel, Nicolai Friis, Martin Ringbauer, and Marcus Huber, "On the role of entanglement in qudit-based circuit compression", Quantum 7, 1141 (2023).

[33] Natalia Herrera Valencia, Suraj Goel, Will McCutcheon, Hugo Defienne, and Mehul Malik, Frontiers in Optics + Laser Science 2021 FTh6D.5 (2021).

[34] Mateus Araújo, Marcus Huber, Miguel Navascués, Matej Pivoluska, and Armin Tavakoli, "Quantum key distribution rates from semidefinite programming", Quantum 7, 1019 (2023).

[35] Isaac Nape, Valeria Rodríguez-Fajardo, Feng Zhu, Hsiao-Chih Huang, Jonathan Leach, and Andrew Forbes, "Measuring dimensionality and purity of high-dimensional entangled states", Nature Communications 12 1, 5159 (2021).

[36] Isaac Nape, André G de Oliveira, Donovan Slabbert, Nicholas Bornman, Jason Francis, Paulo H Souto Ribeiro, and Andrew Forbes, "An all-digital approach for versatile hybrid entanglement generation", Journal of Optics 24 5, 054003 (2022).

[37] Shuheng Liu, Matteo Fadel, Qiongyi He, Marcus Huber, and Giuseppe Vitagliano, "Bounding entanglement dimensionality from the covariance matrix", Quantum 8, 1236 (2024).

[38] Sébastien Designolle, Vatshal Srivastav, Roope Uola, Natalia Herrera Valencia, Will McCutcheon, Mehul Malik, and Nicolas Brunner, "Genuine High-Dimensional Quantum Steering", Physical Review Letters 126 20, 200404 (2021).

[39] Matteo Fadel, Ayaka Usui, Marcus Huber, Nicolai Friis, and Giuseppe Vitagliano, "Entanglement Quantification in Atomic Ensembles", Physical Review Letters 127 1, 010401 (2021).

[40] Vatshal Srivastav, Natalia Herrera Valencia, Will McCutcheon, Sébastien Designolle, Roope Uola, Nicolas Brunner, and Mehul Malik, Frontiers in Optics + Laser Science 2021 LW5F.3 (2021).

[41] 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).

[42] 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).

[43] 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).

[44] 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).

[45] Mehul Malik, Optical Fiber Communication Conference (OFC) 2024 Tu3C.3 (2024) ISBN:978-1-957171-32-6.

[46] 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).

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

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

[49] 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).

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

[51] Nicky Kai Hong Li, Marcus Huber, and Nicolai Friis, "High-dimensional entanglement witnessed by correlations in arbitrary bases", arXiv:2406.04395, (2024).

[52] 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).

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

[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 Multipath Down-Conversion", Physical Review Letters 125 9, 090503 (2020).

[55] 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).

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

[57] 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).

[58] 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).

[59] 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).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-18 11:15:28) and SAO/NASA ADS (last updated successfully 2024-06-18 11:15:30). The list may be incomplete as not all publishers provide suitable and complete citation data.