![](data:image/png;base64,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)
[3] Antonio Ac´ın, Nicolas Brunner, Nicolas Gisin,
Serge Massar, Stefano Pironio, and Valerio
Scarani, Device-Independent Security of Quan-
tum Cryptography against Collective Attacks,
Phys. Rev. Lett. 98, 230501 (2007), arXiv:quant-
ph/0702152.
[4] Marissa Giustina, Marijn A. M. Versteegh, S¨oren
Wengerowsky, Johannes Handsteiner, Armin
Hochrainer, Kevin Phelan, Fabian Steinlech-
ner, Johannes Kofler, Jan-
˚
Ake Larsson, Car-
los Abell´an, Waldimar Amaya, Valerio Pruneri,
Morgan W. Mitchell, J¨orn Beyer, Thomas Ger-
rits, 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 En-
tangled 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 Coak-
ley, Shellee D Dyer, Carson Hodge, Adriana E
Lita, Varun B Verma, Camilla Lambrocco, Ed-
ward Tortorici, Alan L Migdall, Yanbao Zhang,
Daniel R Kumor, William H Farr, Francesco
Marsili, Matthew D Shaw, Jeffrey A Stern, Car-
los Abell´an, 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 lo-
cal 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 distri-
bution with time-bin qudits, Sci. Adv. 3, e1701491
(2017), arXiv:1709.06135.
[8] Mohammad Mirhosseini, Omar S Maga˜na-
Loaiza, Malcolm N O’Sullivan, Brandon Roden-
burg, 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, Fr´ed´eric Bouchard, Lukas
Bulla, Florian Brandt, Oskar Kohout, Fabian
Steinlechner, Robert Fickler, Mehul Malik, Ye-
lena Guryanova, Rupert Ursin, and Mar-
cus 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 Ac´ın, and Stefano
Pironio, Bell Inequalities Tailored to Maximally
Entangled States, Phys. Rev. Lett. 119, 040402
(2017), arXiv:1607.04578.
[12] Tam´as 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 Tira-
nov, S´ebastien Designolle, Florian Fr¨owis, Nico-
las Brunner, Marcus Huber, and Nicolas Gisin,
Quantifying Photonic High-Dimensional Entan-
glement, Phys. Rev. Lett. 118, 110501 (2017),
arXiv:1701.03269.
[17] Alexey Tiranov, S´ebastien Designolle, Em-
manuel Zambrini Cruzeiro, Jonathan Lavoie,
Nicolas Brunner, Mikael Afzelius, Marcus Huber,
and Nicolas Gisin, Quantification of multidimen-
sional 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 Gre-
gory 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 Cort´es, Stefania Sciara, Benjamin
Wetzel, Yanbing Zhang, Alfonso Cino, Sai T
Chu, Brent E Little, David J Moss, Lucia Cas-
pani, Jos´e Aza˜na, and Roberto Morandotti,
On-chip generation of high-dimensional entan-
gled quantum states and their coherent control,
Nature 546, 622 (2017).
[20] Mario Krenn, Marcus Huber, Robert Fickler,
Radek Lapkiewicz, Sven Ramelow, and An-
ton Zeilinger, Generation and confirmation of a
(100 × 100)-dimensional entangled quantum sys-
Accepted in Quantum 2020-12-18, click title to verify. Published under CC-BY 4.0. 9