--- _id: '12911' abstract: - lang: eng text: 'This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.' acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813." article_number: '109963' article_processing_charge: No article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963 apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963 chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023. ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963. mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963. short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023). date_created: 2023-05-07T22:01:02Z date_published: 2023-08-15T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '15' department: - _id: RoSe - _id: JaMa doi: 10.1016/j.jfa.2023.109963 ec_funded: 1 external_id: arxiv: - '2106.11217' isi: - '000990804300001' intvolume: ' 285' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '08' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '9792' relation: earlier_version status: public scopus_import: '1' status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '13177' abstract: - lang: eng text: In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established. acknowledgement: The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. article_processing_charge: No article_type: original author: - first_name: Bobo full_name: Hua, Bobo last_name: Hua - first_name: Matthias full_name: Keller, Matthias last_name: Keller - first_name: Michael full_name: Schwarz, Michael last_name: Schwarz - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361 apa: Hua, B., Keller, M., Schwarz, M., & Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/14361 chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/14361. ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” Proceedings of the American Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023. ista: Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414. mla: Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361. short: B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414. date_created: 2023-07-02T22:00:43Z date_published: 2023-08-01T00:00:00Z date_updated: 2023-11-14T13:07:09Z day: '01' department: - _id: JaMa doi: 10.1090/proc/14361 external_id: arxiv: - '1804.08353' isi: - '000988204400001' intvolume: ' 151' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.1804.08353' month: '08' oa: 1 oa_version: Preprint page: 3401-3414 publication: Proceedings of the American Mathematical Society publication_identifier: eissn: - 1088-6826 issn: - 0002-9939 publication_status: published publisher: American Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Sobolev-type inequalities and eigenvalue growth on graphs with finite measure type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 151 year: '2023' ... --- _id: '13145' abstract: - lang: eng text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes. acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208. article_processing_charge: No article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Eugene full_name: Lytvynov, Eugene last_name: Lytvynov citation: ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528 apa: Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528 chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528. ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023. ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12. mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528. short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12. date_created: 2023-06-18T22:00:48Z date_published: 2023-05-05T00:00:00Z date_updated: 2023-12-13T11:24:57Z day: '05' ddc: - '510' department: - _id: JaMa doi: 10.1214/23-ECP528 external_id: isi: - '001042025400001' file: - access_level: open_access checksum: 4a543fe4b3f9e747cc52167c17bfb524 content_type: application/pdf creator: dernst date_created: 2023-06-19T09:37:40Z date_updated: 2023-06-19T09:37:40Z file_id: '13152' file_name: 2023_ElectronCommProbability_Schiavo.pdf file_size: 271434 relation: main_file success: 1 file_date_updated: 2023-06-19T09:37:40Z has_accepted_license: '1' intvolume: ' 28' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 1-12 project: - _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c grant_number: E208 name: Configuration Spaces over Non-Smooth Spaces publication: Electronic Communications in Probability publication_identifier: eissn: - 1083-589X publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: A Mecke-type characterization of the Dirichlet–Ferguson measure 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) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2023' ... --- _id: '13318' 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. 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. article_processing_charge: No article_type: original author: - first_name: Alexander full_name: Volberg, Alexander last_name: Volberg - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. 2023. doi:10.1007/s00208-023-02680-0 apa: Volberg, A., & Zhang, H. (2023). Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-023-02680-0 chicago: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” Mathematische Annalen. Springer Nature, 2023. https://doi.org/10.1007/s00208-023-02680-0. ieee: A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” Mathematische Annalen. Springer Nature, 2023. ista: Volberg A, Zhang H. 2023. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. mla: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” Mathematische Annalen, Springer Nature, 2023, doi:10.1007/s00208-023-02680-0. short: A. Volberg, H. Zhang, Mathematische Annalen (2023). date_created: 2023-07-30T22:01:03Z date_published: 2023-07-24T00:00:00Z date_updated: 2023-12-13T11:36:20Z day: '24' department: - _id: JaMa doi: 10.1007/s00208-023-02680-0 external_id: arxiv: - '2210.14468' isi: - '001035665500001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00208-023-02680-0 month: '07' oa: 1 oa_version: Published Version project: - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Noncommutative Bohnenblust–Hille inequalities type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '13271' abstract: - lang: eng text: "In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems." acknowledgement: I am grateful to Boguslaw Zegarliński for asking me the questions in [3] and for helpful communication. I also want to thank Paata Ivanisvili for drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous referee for the valuable comments and for pointing out some errors in an earlier version of the paper. This work is partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. article_processing_charge: No article_type: original author: - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Zhang H. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. 2023. doi:10.1007/s00023-023-01345-7 apa: Zhang, H. (2023). Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-023-01345-7 chicago: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-023-01345-7. ieee: H. Zhang, “Some convexity and monotonicity results of trace functionals,” Annales Henri Poincare. Springer Nature, 2023. ista: Zhang H. 2023. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. mla: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” Annales Henri Poincare, Springer Nature, 2023, doi:10.1007/s00023-023-01345-7. short: H. Zhang, Annales Henri Poincare (2023). date_created: 2023-07-23T22:01:15Z date_published: 2023-07-08T00:00:00Z date_updated: 2023-12-13T11:33:46Z day: '08' department: - _id: JaMa doi: 10.1007/s00023-023-01345-7 ec_funded: 1 external_id: arxiv: - '2108.05785' isi: - '001025709100001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2108.05785 month: '07' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Some convexity and monotonicity results of trace functionals type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ...