Links to Recent Papers by Participants that are Related to the Project, with names of project members in boldface. (Links to posters are at the bottom of this page, as well as links to articles that refer to the project.)
 Arthur Jaffe, Chunlan Jiang, Zhengwei Liu, Yunxiang Ren, and Jinsong Wu, Quantum Fourier analysis, arxiv:2002.03477.
 Qi Zhao and You Zhou, Constructing Multipartite Bell inequalities from stabilizers, arXiv:2002.01843.
 Lu Li, Kaifeng Bu, and Junde Wu, Contextual robustness: An operational measure of contextuality, Phys. Rev. A 101, 012120 (2020).
 Pei Zeng, You Zhou, and Zhenhuan Liu, Quantum gate verification and its application in property testing, arXiv:1911.06855.
 Zhengwei Liu, Quantized Graphs and Quantum Error Correction, arXiv:1910.12065.
 Zhengwei Liu, Sebastian Palcaux, and Jinsong Wu, Fusion Bialgebras and Fourier Analysis, arXiv:1910.12059.
 Yunxiang Ren, A generating problem for subfactors, arXiv:1910.09723.
 Bartosz Regula, Kaifeng Bu, Ryuji Takagi, and Zi-Wen Liu, Characterizing one-shot distillation in general resource theories, arXiv:1909.11677.
 Xiaoqin Gao and Zhengwei Liu, Universal Quantum Computation by a Single Photon, arXiv:1909.09535.
 Zhengwei Liu and Jinsong Wu, Non-Commutative Rényi entropic uncertainty principles, arXiv:1904.04292. To appear in Science China Mathematics.
 Zi-Wen Liu, Kaifeng Bu, Ryuji Takagi, One-shot operational quantum resource theory, arXiv:1904.05840, Physical Review Letters 123 (2019), 020401, selected as Editor’s suggestion.
 Arthur Jaffe and Zhengwei Liu, Reflection Positivity for Levin-Wen models, arXiv:1901.10662. To appear in Expositiones Mathematicae.
 Zhengwei Liu, William Norledge, and Adrian Ocneanu, The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations, arXiv:1901.03243.
 Lu Li, Kaifeng Bu and Zi-Wen Liu, Quantifying the resourse content of quantum channels: An operational approach, arXiv:1812.02572.
 Kaifeng Bu and Dax Enshan Koh, Classical simulation of quantum circuits by half Gauss sums, arXiv:1812.00224.
 Fei Wei, Anqie entropy and arithmetic compactification of natural numbers, arXiv:1811.11000.
 Kaifeng Bu, Weichen Gu, and Arthur Jaffe, Duality of graph invariants, arXiv:1810.08633. To appear in Science China Mathematics.
 Fei Wei, Disjointness of Möbius from asymptotically periodic functions, arXiv:1810.07360.
 Ryuji Takagi, Bartosz Regula, Kaifeng Bu, Zi-Wen Liu, and Gerardo Adesso, Operational advantage of quantum resources in subchannel discrimination, arXiv:1809.01672, Physical Review Letters 122 (2019), 140402, selected as Editor’s Suggestion.
 Jordan Nikkel and Yunxiang Ren, On Jones Subgroup of R. Thompson's Group T, arXiv:1710.06972, International Journal of Algebra and Computation 28 (2018), 877–903.
 Kaifeng Bu, Arthur Jaffe, Zhengwei Liu and Jinsong Wu, De Finetti Theorems for Braided Parafermions, arXiv:1805.05990, Communication in Mathematical Physics 373 (2020), 435–456.
 Zhengwei Liu and Jinsong Wu, Antisymmetric Characters and Fourier Duality, arxiv:1805.04783.
 Zhengwei Liu and Jinsong Wu, Extremal Pairs of Young’s Inequality for Kac Algebras, Pacific Journal of Mathematics 295 (2018), 103–121.
 Arthur Jaffe, Reflection Positivity Then and Now, arXiv:1802.07880.
 William Norledge, Singer cyclic lattices of type M, arXiv:1711.09332.
 William Norledge, Quotients of buildings by groups acting freely on chambers, arXiv:1711.09330.
 William Norledge, Quotients of buildings as W-groupoids, arXiv:1710.06968.
 Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu, and Yunxiang Ren, An angle between intermediate subfactors and its rigidity, arXiv:1710.00285, Transactions of the American Mathematical Society 371 (2019), 5973–5991.
 Zhengwei Liu, Scott Morrison, and David Penneys, Lifting shadings on symmetrically self-dual subfactor planar algebras, arXiv:1709.05023. To appear in Contemporary Mathematics.
 Arthur Jaffe and Zhengwei Liu, A Mathematical Picture Language Program, Proceedings of the National Academy of Sciences 115 (2018), 81–86.
 Zhengwei Liu, Quon Language: Surface Algebras and Fourier Duality, arXiv:1707.03995, Communications in Mathematical Physics 366 (2019), 865–894.
 Zhengwei Liu and Feng Xu, Jones-Wassermann subfactors for modular tensor categories, arXiv:1612:08573. To appear in Advances in Mathematics.
 Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Holographic Software for Quantum Networks, Science China Mathematics 61 (2018), 593–626.
 Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Qudit Isotopy, arXiv:1602.02671.
 Zhengwei Liu, Yang-Baxter Relation Planar Algebras, arXiv:1507.06030.
 Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Uncertainty principles for locally compact quantum groups, Journal of Functional Analysis 274 (2018), 2399-2445.
 Zhengwei Liu and David Penneys, The generator conjecture for 3G subfactor planar algebras, Proceedings of the 2014 Maui and 2015 Qinhuangdao Conferences in Honour of Vaughan F.R. Jones' 60th Birthday (2017), 344–366.
 Zhengwei Liu, Simeng Wang, and Jinsong Wu, Young’s inequality for locally compact quantum groups, Journal of Operator Theory 77 (2017), 109–131.
 Zhengwei Liu and Jinsong Wu, Uncertainty principle for Kac algebras, Journal of Mathematical Physics 58 (2017), 052102.
 Zhengwei Liu and Jinsong Wu, The Noncommutative Fourier Transform: A survey, Acta Mathematica Sinica Chinese Series (In honor of the 75th birthday of Bingren Li) 60 (2017), 69–80.
 Zhengwei Liu, and Alex Wozniakowski, and Arthur Jaffe, Quon 3D language for quantum information, Proceedings of the National Academy of Sciences 114 (2017), 2497–2502.
 Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Constructive Simulation and Topological Design of Protocols, New Journal of Physics 19 (2017), 063016.
 Arthur Jaffe and Bas Janssens, Reflection Positive Doubles, Journal of Functional Analysis 272 (2017), 3506–3557.
 Arthur Jaffe and Zhengwei Liu, Planar Para Algebras, Reflection Positivity, Communications in Mathematical Physics 352 (2017), 95–133.
 Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Noncommutative uncertainty principles, arXiv:1408.1165, Journal of Functional Analysis 270 (2016), 264–311.
 Arthur Jaffe and Bas Janssens, Characterization of Reflection Positivity: Majoranas and Spins, Communications in Mathematical Physics 346 (2016), 1021–1050.
 Arthur Jaffe and Fabio L. Pedrocchi, Reflection Positivity for Parafermions, Communications in Mathematical Physics 337 (2015), 455–472.
 Arthur Jaffe, Stochastic Quantization, Reflection Positivity, and Quantum Fields, Journal of Statistical Physics 161 (2015), 1–15.
 Arthur Jaffe, Christian Jäkel, and Roberto Martinez, Complex Classical Fields: an Example, Journal of Functional Analysis 266 (2014), 1833–1881.
Links to Posters by Participants that are Related to the Project.
These may be large files, which take some time to load.
 Harvard Physics Research Scholar Retreat September 12, 2018. Poster by Kaifeng Bu (Awarded first prize)
Links to Articles that Refer to the Project.
 Interview with Zi-Wen Liu about the work of Kaifeng Bu, One-Shot Operational Quantum Resource Theory
 Peter Reuell, Picture Perfect Approach to Science, Harvard Gazette (January 24, 2018).
 Daniel S. Silver, The New Language of Mathematics, American Scientist 105 (November-December 2017), 365.
 Peter Reuell, Making Math More Lego Like, Harvard Gazette (March 2, 2017).