[{"publication":"Mathematische Annalen","status":"public","type":"journal_article","day":"24","date_created":"2023-07-30T22:01:03Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","article_type":"original","date_published":"2023-07-24T00:00:00Z","month":"07","quality_controlled":"1","oa_version":"Published Version","project":[{"name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337"}],"acknowledgement":"The research of A.V. is supported by NSF DMS-1900286, DMS-2154402 and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284 while both authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity program.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"_id":"13318","article_processing_charge":"No","oa":1,"date_updated":"2023-12-13T11:36:20Z","arxiv":1,"author":[{"last_name":"Volberg","full_name":"Volberg, Alexander","first_name":"Alexander"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","last_name":"Zhang","first_name":"Haonan"}],"abstract":[{"lang":"eng","text":"Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes."}],"citation":{"short":"A. Volberg, H. Zhang, Mathematische Annalen (2023).","ista":"Volberg A, Zhang H. 2023. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen.","mla":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>.","ama":"Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>","chicago":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>.","apa":"Volberg, A., &#38; Zhang, H. (2023). Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>","ieee":"A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” <i>Mathematische Annalen</i>. Springer Nature, 2023."},"publication_status":"epub_ahead","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00208-023-02680-0"}],"isi":1,"title":"Noncommutative Bohnenblust–Hille inequalities","external_id":{"arxiv":["2210.14468"],"isi":["001035665500001"]},"doi":"10.1007/s00208-023-02680-0","year":"2023"},{"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"ddc":["510"],"year":"2022","doi":"10.1007/s00208-021-02331-2","ec_funded":1,"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","external_id":{"arxiv":["2110.05137"],"isi":["000734150200001"]},"arxiv":1,"oa":1,"date_updated":"2023-08-02T13:39:05Z","volume":384,"article_processing_charge":"Yes (via OA deal)","_id":"10588","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","quality_controlled":"1","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","citation":{"short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. 2022;384:1815-1832. doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>.","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” <i>Mathematische Annalen</i>, vol. 384. Springer Nature, pp. 1815–1832, 2022."},"abstract":[{"lang":"eng","text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds."}],"keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"has_accepted_license":"1","department":[{"_id":"JaMa"}],"file":[{"creator":"alisjak","file_id":"10596","content_type":"application/pdf","relation":"main_file","success":1,"date_updated":"2022-01-03T11:08:31Z","access_level":"open_access","date_created":"2022-01-03T11:08:31Z","checksum":"2593abbf195e38efa93b6006b1e90eb1","file_name":"2021_MathAnn_DelloSchiavo.pdf","file_size":410090}],"date_created":"2022-01-02T23:01:35Z","month":"12","date_published":"2022-12-01T00:00:00Z","article_type":"original","publisher":"Springer Nature","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Mathematische Annalen","file_date_updated":"2022-01-03T11:08:31Z","page":"1815-1832","day":"01","type":"journal_article","intvolume":"       384","status":"public"}]