We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond being unbiased, thus enabling entanglement quantification with minimal assumptions. Furthermore, we show that it is feasible to experimentally implement our method with readily available equipment and even conservative estimates of physical parameters.
 C. H. Bennett, P. W. Shor, J. A. Smolin, A. V. Thapliyal, IEEE Transactions on Information Theory, Vol. 48 (10), 2637 - 2655 (2002), 10.1109/TIT.2002.802612.
 C. Bernhard, B. Bessire, A. Montina, M. Pfaffhauser, A. Stefanov and S. Wolf, J. of Phys. A: Math. and Theor., 47(42):424013 (2014), 10.1088/1751-8113/47/42/424013.
 L. Gurvits, Classical deterministic complexity of Edmonds' problem and quantum entanglement in Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, 10 (2003), 10.1145/780542.780545.
 David Sauerwein, Chiara Macchiavello, Lorenzo Maccone, and Barbara Kraus, "Multipartite correlations in mutually unbiased bases", Physical Review A 95 4, 042315 (2017).
 Anthony Martin, Thiago Guerreiro, Alexey Tiranov, Sébastien Designolle, Florian Fröwis, Nicolas Brunner, Marcus Huber, and Nicolas Gisin, "Quantifying Photonic High-Dimensional Entanglement", Physical Review Letters 118 11, 110501 (2017).
 Yu Guo, Xiao-Min Hu, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, and Guang-Can Guo, "Experimental witness of genuine high-dimensional entanglement", Physical Review A 97 6, 062309 (2018).
 Michał Dąbrowski, Matuesz Mazelanik, Michał Parniak, Adam Leszczyński, Michał Lipka, and Wojciech Wasilewski, "Certification of high-dimensional entanglement and Einstein-Podolsky-Rosen steering with cold atomic quantum memory", Physical Review A 98 4, 042126 (2018).
 James Schneeloch and Gregory A. Howland, "Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations", Physical Review A 97 4, 042338 (2018).
 Nicolai Friis, Giuseppe Vitagliano, Mehul Malik, and Marcus Huber, "Entanglement certification from theory to experiment", Nature Reviews Physics 1 1, 72 (2019).
 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", Physical Review A 96 4, 040303 (2017).
 Takuya Ikuta and Hiroki Takesue, "Four-dimensional entanglement distribution over 100 km", Scientific Reports 8 1, 817 (2018).
 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", Nature Physics 14 10, 1032 (2018).
 D. S. Tasca, Łukasz Rudnicki, R. S. Aspden, M. J. Padgett, P. H. Souto Ribeiro, and S. P. Walborn, "Testing for entanglement with periodic coarse graining", Physical Review A 97 4, 042312 (2018).
 Fabricio Toscano, Daniel Tasca, Łukasz Rudnicki, and Stephen Walborn, "Uncertainty Relations for Coarse–Grained Measurements: An Overview", Entropy 20 6, 454 (2018).
 Vahid Ansari, John M. Donohue, Benjamin Brecht, and Christine Silberhorn, "Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings", Optica 5 5, 534 (2018).
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