{"ddc":["530"],"doi":"10.1103/physrevx.14.031035","quality_controlled":"1","title":"Many-body entropies and entanglement from polynomially many local measurements","day":"26","publication":"Physical Review X","date_updated":"2024-09-05T09:42:47Z","article_number":"031035","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","intvolume":"        14","volume":14,"project":[{"grant_number":"850899","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","call_identifier":"H2020"}],"_id":"17493","has_accepted_license":"1","scopus_import":"1","article_type":"original","issue":"3","author":[{"first_name":"Benoît","last_name":"Vermersch","full_name":"Vermersch, Benoît"},{"orcid":"0000-0003-0038-7068","first_name":"Marko","full_name":"Ljubotina, Marko","last_name":"Ljubotina","id":"F75EE9BE-5C90-11EA-905D-16643DDC885E"},{"first_name":"J. Ignacio","last_name":"Cirac","full_name":"Cirac, J. Ignacio"},{"last_name":"Zoller","full_name":"Zoller, Peter","first_name":"Peter"},{"orcid":"0000-0002-2399-5827","first_name":"Maksym","full_name":"Serbyn, Maksym","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Lorenzo","last_name":"Piroli","full_name":"Piroli, Lorenzo"}],"publication_identifier":{"issn":["2160-3308"]},"ec_funded":1,"publication_status":"published","date_created":"2024-09-04T18:57:11Z","oa":1,"status":"public","abstract":[{"lang":"eng","text":"Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms."}],"oa_version":"Published Version","file_date_updated":"2024-09-05T09:39:00Z","type":"journal_article","external_id":{"arxiv":["2311.08108"]},"acknowledgement":"B. V. acknowledges funding from the Austrian Science Foundation (Grant No. FWF, P 32597 N), from the French National Research Agency via the JCJC project QRand (Grant No. ANR-20-CE47-0005), and via the research programs Plan France 2030 EPIQ (Grant No. ANR-22-PETQ-0007), QUBITAF (Grant No. ANR-22-PETQ-0004), and HQI (Grant No. ANR-22-PNCQ-0002). M. L. and M. S. acknowledge support by the European Research Council under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899). M. S. acknowledges the hospitality of KITP supported in part by the National Science Foundation under Grants No. NSF PHY-1748958 and No. NSF PHY-2309135. J. I. C. is supported by the Hightech Agenda Bayern Plus through the Munich Quantum Valley and the German Federal Ministry of Education and Research through EQUAHUMO (Grant No. 13N16066). P. Z. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 101113690 (PASQuanS2.1).","publisher":"American Physical Society","language":[{"iso":"eng"}],"year":"2024","department":[{"_id":"MaSe"}],"date_published":"2024-08-26T00:00:00Z","month":"08","article_processing_charge":"No","citation":{"short":"B. Vermersch, M. Ljubotina, J.I. Cirac, P. Zoller, M. Serbyn, L. Piroli, Physical Review X 14 (2024).","ista":"Vermersch B, Ljubotina M, Cirac JI, Zoller P, Serbyn M, Piroli L. 2024. Many-body entropies and entanglement from polynomially many local measurements. Physical Review X. 14(3), 031035.","ieee":"B. Vermersch, M. Ljubotina, J. I. Cirac, P. Zoller, M. Serbyn, and L. Piroli, “Many-body entropies and entanglement from polynomially many local measurements,” <i>Physical Review X</i>, vol. 14, no. 3. American Physical Society, 2024.","mla":"Vermersch, Benoît, et al. “Many-Body Entropies and Entanglement from Polynomially Many Local Measurements.” <i>Physical Review X</i>, vol. 14, no. 3, 031035, American Physical Society, 2024, doi:<a href=\"https://doi.org/10.1103/physrevx.14.031035\">10.1103/physrevx.14.031035</a>.","apa":"Vermersch, B., Ljubotina, M., Cirac, J. I., Zoller, P., Serbyn, M., &#38; Piroli, L. (2024). Many-body entropies and entanglement from polynomially many local measurements. <i>Physical Review X</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevx.14.031035\">https://doi.org/10.1103/physrevx.14.031035</a>","chicago":"Vermersch, Benoît, Marko Ljubotina, J. Ignacio Cirac, Peter Zoller, Maksym Serbyn, and Lorenzo Piroli. “Many-Body Entropies and Entanglement from Polynomially Many Local Measurements.” <i>Physical Review X</i>. American Physical Society, 2024. <a href=\"https://doi.org/10.1103/physrevx.14.031035\">https://doi.org/10.1103/physrevx.14.031035</a>.","ama":"Vermersch B, Ljubotina M, Cirac JI, Zoller P, Serbyn M, Piroli L. Many-body entropies and entanglement from polynomially many local measurements. <i>Physical Review X</i>. 2024;14(3). doi:<a href=\"https://doi.org/10.1103/physrevx.14.031035\">10.1103/physrevx.14.031035</a>"},"file":[{"relation":"main_file","date_created":"2024-09-05T09:39:00Z","creator":"cchlebak","file_size":1408836,"access_level":"open_access","success":1,"date_updated":"2024-09-05T09:39:00Z","content_type":"application/pdf","file_id":"17532","file_name":"2024_PhysRevX_Vermersch.pdf","checksum":"1b114acc89025120727200681e4e9074"}]}