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.
 Yu Guo, Xiao-Min Hu, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, 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, 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, Gregory A. Howland, "Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations", Physical Review A 97 4, 042338 (2018).
 Alexey Tiranov, Sébastien Designolle, Emmanuel Zambrini Cruzeiro, Jonathan Lavoie, Nicolas Brunner, Mikael Afzelius, Marcus Huber, Nicolas Gisin, "Quantification of multidimensional entanglement stored in a crystal", Physical Review A 96 4, 040303 (2017).
 Takuya Ikuta, 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, 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, S. P. Walborn, "Testing for entanglement with periodic coarse graining", Physical Review A 97 4, 042312 (2018).
 Fabricio Toscano, Daniel Tasca, Łukasz Rudnicki, Stephen Walborn, "Uncertainty Relations for Coarse–Grained Measurements: An Overview", Entropy 20 6, 454 (2018).
 Vahid Ansari, John M. Donohue, Benjamin Brecht, Christine Silberhorn, "Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings", Optica 5 5, 534 (2018).
(The above data is from Crossref's cited-by service. Unfortunately not all publishers provide suitable and complete citation data so that some citing works or bibliographic details may be missing.)
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.