{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T18:24:51Z","timestamp":1765045491972,"version":"3.37.3"},"reference-count":68,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T00:00:00Z","timestamp":1672012800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T00:00:00Z","timestamp":1672012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0012704"],"award-info":[{"award-number":["DE-SC0012704"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0012704"],"award-info":[{"award-number":["DE-SC0012704"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC05-00OR22725"],"award-info":[{"award-number":["DE-AC05-00OR22725"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["ERKJ353"],"award-info":[{"award-number":["ERKJ353"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-19-2-0087"],"award-info":[{"award-number":["W911NF-19-2-0087"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-20-2-0168"],"award-info":[{"award-number":["W911NF-20-2-0168"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s42484-022-00088-8","type":"journal-article","created":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T14:06:42Z","timestamp":1672063602000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Dimension-adaptive machine learning-based quantum state reconstruction"],"prefix":"10.1007","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0699-0669","authenticated-orcid":false,"given":"Sanjaya","family":"Lohani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7857-4253","authenticated-orcid":false,"given":"Sangita","family":"Regmi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9650-4462","authenticated-orcid":false,"given":"Joseph M.","family":"Lukens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryan T.","family":"Glasser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0532-7884","authenticated-orcid":false,"given":"Thomas A.","family":"Searles","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2698-9887","authenticated-orcid":false,"given":"Brian T.","family":"Kirby","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,12,26]]},"reference":[{"key":"88_CR1","doi-asserted-by":"publisher","first-page":"140502","DOI":"10.1103\/PhysRevLett.127.140502","volume":"127","author":"S Ahmed","year":"2021","unstructured":"Ahmed S, Mu\u00f1oz CS, Nori F, Kockum AF (2021) Quantum state tomography with conditional generative adversarial networks. Phys Rev Lett 127:140502","journal-title":"Phys Rev Lett"},{"key":"88_CR2","doi-asserted-by":"publisher","first-page":"033278","DOI":"10.1103\/PhysRevResearch.3.033278","volume":"3","author":"S Ahmed","year":"2021","unstructured":"Ahmed S, Mu\u00f1oz CS, Nori F, Kockum AF (2021) Classification and reconstruction of optical quantum states with deep neural networks. Phys Rev Research 3:033278","journal-title":"Phys Rev Research"},{"key":"88_CR3","doi-asserted-by":"publisher","first-page":"055302","DOI":"10.1088\/1751-8113\/43\/5\/055302","volume":"43","author":"V Al Osipov","year":"2010","unstructured":"Al Osipov V, Sommersand H-J, Zyczkowski K (2010) Random Bures mixed states and the distribution of their purity. J Phys A: Math Theor 43:055302","journal-title":"J Phys A: Math Theor"},{"key":"88_CR4","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/S1049-250X(05)52003-2","volume":"52","author":"JB Altepeter","year":"2005","unstructured":"Altepeter JB, Jeffrey ER, Kwiat PG (2005) Photonic state tomography. Adv At Mol Opt Phys 52:105","journal-title":"Adv At Mol Opt Phys"},{"key":"88_CR5","doi-asserted-by":"publisher","first-page":"010304","DOI":"10.1103\/PhysRevA.61.010304","volume":"61","author":"K Banaszek","year":"1999","unstructured":"Banaszek K, D\u2019Ariano GM, Paris MGA, Sacchi MF (1999) Maximum-likelihood estimation of the density matrix. Phys Rev A 61:010304","journal-title":"Phys Rev A"},{"key":"88_CR6","doi-asserted-by":"publisher","first-page":"043034","DOI":"10.1088\/1367-2630\/12\/4\/043034","volume":"12","author":"R Blume-Kohout","year":"2010","unstructured":"Blume-Kohout R (2010) Optimal, reliable estimation of quantum states. New J Phys 12:043034","journal-title":"New J Phys"},{"key":"88_CR7","doi-asserted-by":"publisher","first-page":"190403","DOI":"10.1103\/PhysRevLett.127.190403","volume":"127","author":"S Borah","year":"2021","unstructured":"Borah S, Sarma B, Kewming M, Milburn GJ, Twamley J (2021) Measurement-Based Feedback Quantum Control with Deep Reinforcement Learning for a Double-Well Nonlinear Potential. Phys Rev Lett 127:190403","journal-title":"Phys Rev Lett"},{"key":"88_CR8","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1038\/s42256-019-0028-1","volume":"1","author":"J Carrasquilla","year":"2019","unstructured":"Carrasquilla J, Torlai G, Melko RG, Aolita L (2019) Reconstructing quantum states with generative models. Nat Mach Intell 1:155","journal-title":"Nat Mach Intell"},{"key":"88_CR9","doi-asserted-by":"publisher","first-page":"15184","DOI":"10.1364\/OE.456597","volume":"30","author":"JC Chapman","year":"2022","unstructured":"Chapman JC, Lukens JM, Qi B, Pooser RC, Peters NA (2022) Bayesian homodyne and heterodyne tomography. Opt Express 30:15184","journal-title":"Opt Express"},{"key":"88_CR10","doi-asserted-by":"publisher","first-page":"035014","DOI":"10.1088\/2632-2153\/abe5f5","volume":"2","author":"O Danaci","year":"2021","unstructured":"Danaci O, Lohani S, Kirby BT, Glasser RT (2021) Machine learning pipeline for quantum state estimation with incomplete measurements. Mach Learn Sci Technol 2:035014","journal-title":"Mach Learn Sci Technol"},{"key":"88_CR11","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1038\/s42254-020-0186-4","volume":"2","author":"J Eisert","year":"2020","unstructured":"Eisert J, Hangleiter D, Walk N, Roth I, Markham D, Parekh R, Chabaud U, Kashefi E (2020) Quantum certification and benchmarking. Nat Rev Phys 2:382","journal-title":"Nat Rev Phys"},{"key":"88_CR12","doi-asserted-by":"publisher","first-page":"217901","DOI":"10.1103\/PhysRevLett.88.217901","volume":"88","author":"AK Ekert","year":"2002","unstructured":"Ekert AK, Alves CM, Oi DK, Horodecki M, Horodecki P, Kwek LC (2002) Direct estimations of linear and nonlinear functionals of a quantum state. Phys Rev Lett 88:217901","journal-title":"Phys Rev Lett"},{"key":"88_CR13","doi-asserted-by":"publisher","first-page":"230501","DOI":"10.1103\/PhysRevLett.106.230501","volume":"106","author":"ST Flammia","year":"2011","unstructured":"Flammia ST , Liu Y-K (2011) Direct Fidelity Estimation from Few Pauli Measurements. Phys Rev Lett 106:230501","journal-title":"Phys Rev Lett"},{"key":"88_CR14","doi-asserted-by":"publisher","first-page":"040355","DOI":"10.1103\/PRXQuantum.2.040355","volume":"2","author":"\u00c9 Genois","year":"2021","unstructured":"Genois \u00c9, Gross JA, Di Paolo A, Stevenson NJ, Koolstra G, Hashim A, Siddiqi I, Blais A (2021) Quantum-tailored machine-learning characterization of a superconducting qubit. PRX Quantum 2:040355","journal-title":"PRX Quantum"},{"key":"88_CR15","doi-asserted-by":"publisher","first-page":"160401","DOI":"10.1103\/PhysRevLett.124.160401","volume":"124","author":"T Giordani","year":"2020","unstructured":"Giordani T, Suprano A, Polino E, Acanfora F, Innocenti L, Ferraro A, Paternostro M, Spagnolo N, Sciarrino F (2020) Machine learning-based classification of vector vortex beams. Phys Rev Lett 124:160401","journal-title":"Phys Rev Lett"},{"key":"88_CR16","doi-asserted-by":"publisher","first-page":"033024","DOI":"10.1088\/1367-2630\/18\/3\/033024","volume":"18","author":"C Granade","year":"2016","unstructured":"Granade C, Combes J, Cory DG (2016) Practical Bayesian tomography. New J Phys 18:033024","journal-title":"New J Phys"},{"key":"88_CR17","doi-asserted-by":"publisher","first-page":"150401","DOI":"10.1103\/PhysRevLett.105.150401","volume":"105","author":"D Gross","year":"2010","unstructured":"Gross D, Liu Y-K, Flammia ST, Becker S, Eisert J (2010) Quantum state tomography via compressed sensing. Phys Rev Lett 105:150401","journal-title":"Phys Rev Lett"},{"key":"88_CR18","doi-asserted-by":"publisher","first-page":"010318","DOI":"10.1103\/PRXQuantum.2.010318","volume":"2","author":"R Gupta","year":"2021","unstructured":"Gupta R, Xia R, Levine RD, Kais S (2021) Maximal entropy approach for quantum state tomography. PRX Quantum 2:010318","journal-title":"PRX Quantum"},{"key":"88_CR19","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1038\/nature04279","volume":"438","author":"H H\u00e4ffner","year":"2005","unstructured":"H\u00e4ffner H, H\u00e4nsel W, Roos CF, Benhelm J, Chek-al-kar D, Chwalla M, K\u00f6rber T, Rapol UD, Riebe M, Schmidt PO, Becher C, G\u00fchne O, D\u00fcr W, Blatt R (2005) Scalable multiparticle entanglement of trapped ions. Nature 438:643","journal-title":"Nature"},{"key":"88_CR20","doi-asserted-by":"publisher","first-page":"083036","DOI":"10.1088\/1367-2630\/18\/8\/083036","volume":"18","author":"Z Hou","year":"2016","unstructured":"Hou Z, Zhong H-S, Tian Y, Dong D, Qi B, Li L, Wang Y, Nori F, Xiang G-Y, Li C-F, Guo G-C (2016) Full reconstruction of a 14-qubit state within four hours. New J Phys 18:083036","journal-title":"New J Phys"},{"key":"88_CR21","doi-asserted-by":"publisher","first-page":"R1561","DOI":"10.1103\/PhysRevA.55.R1561","volume":"55","author":"Z Hradil","year":"1997","unstructured":"Hradil Z (1997) Quantum-state estimation. Phys Rev A 55:R1561","journal-title":"Phys Rev A"},{"key":"88_CR22","doi-asserted-by":"publisher","first-page":"874","DOI":"10.3390\/sym14050874","volume":"14","author":"H-Y Hsieh","year":"2022","unstructured":"Hsieh H-Y, Ning J, Chen Y-R, Wu H-C, Chen HL, Wu C-M, Lee R-K (2022) Direct Parameter Estimations from Machine Learning-Enhanced Quantum State Tomography. Symmetry 14: 874","journal-title":"Symmetry"},{"key":"88_CR23","doi-asserted-by":"publisher","first-page":"1050","DOI":"10.1038\/s41567-020-0932-7","volume":"16","author":"H-Y Huang","year":"2020","unstructured":"Huang H-Y, kuengand R, Preskill J (2020) Predicting many properties of a quantum system from very few measurements. Nat Phys 16:1050","journal-title":"Nat Phys"},{"key":"88_CR24","doi-asserted-by":"publisher","first-page":"052120","DOI":"10.1103\/PhysRevA.85.052120","volume":"85","author":"F Husz\u00e1r","year":"2012","unstructured":"Husz\u00e1r F , Houlsby NMT (2012) Adaptive Bayesian quantum tomography. Phys Rev A 85:052120","journal-title":"Phys Rev A"},{"key":"88_CR25","doi-asserted-by":"publisher","first-page":"052312","DOI":"10.1103\/PhysRevA.64.052312","volume":"64","author":"DFV James","year":"2001","unstructured":"James DFV, Kwiat PG, Munro WJ, White AG (2001) Measurement of qubits. Phys Rev A 64:052312","journal-title":"Phys Rev A"},{"key":"88_CR26","doi-asserted-by":"crossref","unstructured":"James DF, Kwiat PG, Munro WJ, White AG (2005) On the measurement of qubits. In: Asymptotic theory of quantum statistical inference: selected papers. World Scientific, pp 509\u2013538","DOI":"10.1142\/9789812563071_0035"},{"key":"88_CR27","doi-asserted-by":"publisher","first-page":"012409","DOI":"10.1103\/PhysRevA.106.012409","volume":"106","author":"D Koutny\u0300","year":"2022","unstructured":"Koutny\u0300 D, Motka L, Hradil Z, \u0158,eh\u00e1\u010dek J, S\u00e1nchez-Soto LL (2022) Neural-network quantum state tomography. Phys Rev A 106:012409","journal-title":"Phys Rev A"},{"key":"88_CR28","doi-asserted-by":"publisher","first-page":"062122","DOI":"10.1103\/PhysRevA.87.062122","volume":"87","author":"KS Kravtsov","year":"2013","unstructured":"Kravtsov KS, Straupe SS, Radchenko IV, Houlsby NMT, Husz\u00e1r F, Kulik SP (2013) Experimental adaptive Bayesian tomography. Phys Rev A 87:062122","journal-title":"Phys Rev A"},{"key":"88_CR29","doi-asserted-by":"publisher","first-page":"170403","DOI":"10.1103\/PhysRevLett.108.170403","volume":"108","author":"W-T Liu","year":"2012","unstructured":"Liu W-T, Zhang T, Liu J-Y, Chen P-X, Yuan J-M (2012) Experimental quantum state tomography via compressed sampling. Phys Rev Lett 108:170403","journal-title":"Phys Rev Lett"},{"key":"88_CR30","doi-asserted-by":"publisher","first-page":"035007","DOI":"10.1088\/2632-2153\/ab9a21","volume":"1","author":"S Lohani","year":"2020","unstructured":"Lohani S, Kirby BT, Brodsky M, Danaci O, Glasser RT (2020) Machine learning assisted quantum state estimation. Mach Learn Sci Technol 1:035007","journal-title":"Mach Learn Sci Technol"},{"key":"88_CR31","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1038\/s42005-020-00444-9","volume":"3","author":"S Lohani","year":"2020","unstructured":"Lohani S, Knutson EM, Glasser RT (2020) Generative machine learning for robust free-space communication. Commun Phys 3:177","journal-title":"Commun Phys"},{"key":"88_CR32","doi-asserted-by":"publisher","first-page":"04LT01","DOI":"10.1088\/2632-2153\/ac9036","volume":"3","author":"S Lohani","year":"2022","unstructured":"Lohani S, Lukens JM, Glasser RT, Searles TA, Kirby BT (2022) Data-centric machine learning in quantum information science. Mach Learn Sci Technol 3:04LT01","journal-title":"Mach Learn Sci Technol"},{"key":"88_CR33","doi-asserted-by":"publisher","first-page":"043145","DOI":"10.1103\/PhysRevResearch.3.043145","volume":"3","author":"S Lohani","year":"2021","unstructured":"Lohani S, Lukens JM, Jones DE, Searles TA, Glasser RT, Kirby BT (2021) Improving application performance with biased distributions of quantum states. Phys Rev Research 3: 043145","journal-title":"Phys Rev Research"},{"key":"88_CR34","doi-asserted-by":"publisher","first-page":"2103410","DOI":"10.1109\/TQE.2021.3106958","volume":"2","author":"S Lohani","year":"2021","unstructured":"Lohani S, Searles TA, Kirby BT, Glasser R (2021) On the experimental feasibility of quantum state reconstruction via machine learning. IEEE Trans Quantum Eng 2:2103410","journal-title":"IEEE Trans Quantum Eng"},{"key":"88_CR35","doi-asserted-by":"publisher","first-page":"012315","DOI":"10.1103\/PhysRevA.98.012315","volume":"98","author":"S Lu","year":"2018","unstructured":"Lu S, Huang S, Li K, Li J, Chen J, Lu D, Ji Z, shen Y, Zhou D, Zeng B (2018) Separability-entanglement classifier via machine learning. Phys Rev A 98:012315","journal-title":"Phys Rev A"},{"key":"88_CR36","doi-asserted-by":"publisher","first-page":"4338","DOI":"10.1038\/s41467-022-31639-z","volume":"13","author":"H-H Lu","year":"2022","unstructured":"Lu H-H, Myilswamy KV, Bennink RS, Seshadri S, Alshaykh MS, Liu J, Kippenberg TJ, Leaird DE, Weiner AM, Lukens JM (2022) Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements. Nat Commun 13:4338","journal-title":"Nat Commun"},{"key":"88_CR37","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1038\/s41534-021-00447-6","volume":"7","author":"JM Lukens","year":"2021","unstructured":"Lukens JM, Law KJ, Bennink RS (2021) A Bayesian analysis of classical shadows. npj Quantum Inf 7:113","journal-title":"npj Quantum Inf"},{"key":"88_CR38","doi-asserted-by":"publisher","first-page":"063038","DOI":"10.1088\/1367-2630\/ab8efa","volume":"22","author":"JM Lukens","year":"2020","unstructured":"Lukens JM, Law KJH, Jasra A, Lougovski P (2020) A practical and efficient approach for Bayesian quantum state estimation. New J Phys 22:063038","journal-title":"New J Phys"},{"key":"88_CR39","doi-asserted-by":"publisher","first-page":"S556","DOI":"10.1088\/1464-4266\/6\/6\/014","volume":"6","author":"AI Lvovsky","year":"2004","unstructured":"Lvovsky AI (2004) Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J Opt B: Quantum Semiclass Opt 6:S556","journal-title":"J Opt B: Quantum Semiclass Opt"},{"key":"88_CR40","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.jspi.2016.11.003","volume":"184","author":"TT Mai","year":"2017","unstructured":"Mai TT, Alquier P (2017) Pseudo-Bayesian quantum tomography with rank-adaptation. J Stat Plan Inference 184:62. ISSN 0378-3758","journal-title":"J Stat Plan Inference"},{"key":"88_CR41","doi-asserted-by":"publisher","first-page":"022412","DOI":"10.1103\/PhysRevA.102.022412","volume":"102","author":"A Melkani","year":"2020","unstructured":"Melkani A, Gneiting C, Nori F (2020) Eigenstate extraction with neural-network tomography. Phys Rev A 102:022412","journal-title":"Phys Rev A"},{"key":"88_CR42","doi-asserted-by":"publisher","first-page":"032126","DOI":"10.1103\/PhysRevA.81.032126","volume":"81","author":"ST Merkel","year":"2010","unstructured":"Merkel ST, Riofrio CA, Flammia ST, Deutsch IH (2010) Random unitary maps for quantum state reconstruction. Phys Rev A 81:032126","journal-title":"Phys Rev A"},{"key":"88_CR43","doi-asserted-by":"publisher","first-page":"042604","DOI":"10.1103\/PhysRevA.102.042604","volume":"102","author":"M Neugebauer","year":"2020","unstructured":"Neugebauer M, Fischer L, J\u00e4ger A, Czischek S, Jochim S, Weidem\u00fcller M, G\u00e4rttner M (2020) Neural-network quantum state tomography in a two-qubit experiment. Phys Rev A 102:042604","journal-title":"Phys Rev A"},{"key":"88_CR44","unstructured":"Nielsen MA (1996) The entanglement fidelity and quantum error correction. arXiv:quant-ph\/9606012"},{"key":"88_CR45","doi-asserted-by":"publisher","first-page":"042120","DOI":"10.1103\/PhysRevA.76.042120","volume":"76","author":"S Olivares","year":"2007","unstructured":"Olivares S, Paris MG (2007) Quantum estimation via the minimum Kullback entropy principle. Phys Rev A 76:042120","journal-title":"Phys Rev A"},{"key":"88_CR46","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1038\/s41534-020-0248-6","volume":"6","author":"AM Palmieri","year":"2020","unstructured":"Palmieri AM, Kovlakov E, Bianchi F, Yudin D, Straupe S, Biamonte JD, Kulik S (2020) Experimental neural network enhanced quantum tomography. npj Quantum Inf 6:20","journal-title":"npj Quantum Inf"},{"key":"88_CR47","doi-asserted-by":"publisher","first-page":"3496","DOI":"10.1038\/srep03496","volume":"3","author":"B Qi","year":"2013","unstructured":"Qi B, Hou Z, Li L, Dong D, Xiang G, Guo G (2013) Quantum state tomography via linear regression estimation. Sci Rep 3:3496","journal-title":"Sci Rep"},{"key":"88_CR48","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1038\/s41534-021-00436-9","volume":"7","author":"Y Quek","year":"2021","unstructured":"Quek Y, Fort S, Ng HK (2021) Adaptive quantum state tomography with neural networks. npj Quantum Inf 7:105","journal-title":"npj Quantum Inf"},{"key":"88_CR49","doi-asserted-by":"publisher","first-page":"052321","DOI":"10.1103\/PhysRevA.70.052321","volume":"70","author":"J \u0158eh\u00e1\u010dek","year":"2004","unstructured":"\u0158eh\u00e1\u010dek J, Englert B-G , Kaszlikowski D (2004) Minimal qubit tomography. Phys Rev A 70:052321","journal-title":"Phys Rev A"},{"key":"88_CR50","doi-asserted-by":"publisher","first-page":"062325","DOI":"10.1103\/PhysRevA.86.062325","volume":"86","author":"D Rosset","year":"2012","unstructured":"Rosset D, Ferretti-Sch\u00f6bitz R, Bancal J-D, Gisin N, Liang Y-C (2012) Imperfect measurement settings: implications for quantum state tomography and entanglement witnesses. Phys Rev A 86:062325","journal-title":"Phys Rev A"},{"key":"88_CR51","doi-asserted-by":"publisher","first-page":"043018","DOI":"10.1088\/1367-2630\/17\/4\/043018","volume":"17","author":"Y-L Seah","year":"2015","unstructured":"Seah Y-L, Shang J, Ng HK, Nott DJ, Englert B-G (2015) Monte Carlo sampling from the quantum state space, II. New J Phys 17:043018","journal-title":"New J Phys"},{"key":"88_CR52","doi-asserted-by":"publisher","first-page":"2886","DOI":"10.1364\/OL.392694","volume":"45","author":"EM Simmerman","year":"2020","unstructured":"Simmerman EM, Lu H-H, Weiner AM, Lukens JM (2020) Efficient compressive and Bayesian characterization of biphoton frequency spectra. Opt Lett 45:2886","journal-title":"Opt Lett"},{"key":"88_CR53","doi-asserted-by":"publisher","first-page":"070502","DOI":"10.1103\/PhysRevLett.108.070502","volume":"108","author":"JA Smolin","year":"2012","unstructured":"Smolin JA, Gambetta JM, Smith G (2012) Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise. Phys Rev Lett 108:070502","journal-title":"Phys Rev Lett"},{"key":"88_CR54","doi-asserted-by":"publisher","first-page":"10083","DOI":"10.1088\/0305-4470\/36\/39\/308","volume":"36","author":"H-J Sommers","year":"2003","unstructured":"Sommers H-J, Zyczkowski K (2003) Bures volume of the set of mixed quantum states. J Phys A: Math Gen 36:10083","journal-title":"J Phys A: Math Gen"},{"key":"88_CR55","doi-asserted-by":"publisher","first-page":"022311","DOI":"10.1103\/PhysRevA.86.022311","volume":"86","author":"C Spengler","year":"2012","unstructured":"Spengler C, Huber M, Brierley S, Adaktylos T, Hiesmayr BC (2012) Entanglement detection via mutually unbiased bases. Phys Rev A 86:022311","journal-title":"Phys Rev A"},{"key":"88_CR56","doi-asserted-by":"publisher","first-page":"103021","DOI":"10.1088\/1367-2630\/ac1fcb","volume":"23","author":"YS Teo","year":"2021","unstructured":"Teo YS, Shin S, Jeong H, Kim Y, Kim Y-H, Struchalin GI, Kovlakov EV, Straupe SS, Kulik SP, Leuchs G, S\u00e1nchez-Soto LL (2021) Benchmarking quantum tomography completeness and fidelity with machine learning. New J Phys 23:103021","journal-title":"New J Phys"},{"key":"88_CR57","doi-asserted-by":"publisher","first-page":"012303","DOI":"10.1103\/PhysRevA.66.012303","volume":"66","author":"RT Thew","year":"2002","unstructured":"Thew RT, Nemoto K, White AG, Munro WJ (2002) Qudit quantum-state tomography. Phys Rev A 66:012303","journal-title":"Phys Rev A"},{"key":"88_CR58","first-page":"448","volume":"7","author":"ES Tiunov","year":"2020","unstructured":"Tiunov ES, Tiunova V, Ulanov AE, Lvovsky A (2020) Experimental quantum homodyne tomography via machine learning. A Fedorov, Optica 7:448","journal-title":"A Fedorov, Optica"},{"key":"88_CR59","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1038\/s41567-018-0048-5","volume":"14","author":"G Torlai","year":"2018","unstructured":"Torlai G, Mazzola G, Carrasquilla J, Troyer M, Melkoand R, Carleo G (2018) Neural-network quantum state tomography. Nat Phys 14:447","journal-title":"Nat Phys"},{"key":"88_CR60","doi-asserted-by":"publisher","first-page":"230504","DOI":"10.1103\/PhysRevLett.123.230504","volume":"123","author":"G Torlai","year":"2019","unstructured":"Torlai G, Timar B, van Nieuwenburg EPL, Levine H, Omran A, Keesling A, Bernien Greiner H, Vuleti\u0107 V, Lukin MD, Melko RG, Endres M (2019) Integrating Neural Networks with a Quantum Simulator for State Reconstruction. Phys Rev Lett 123: 230504","journal-title":"Phys Rev Lett"},{"key":"88_CR61","doi-asserted-by":"publisher","first-page":"015010","DOI":"10.1088\/2058-9565\/ac3460","volume":"7","author":"R Wang","year":"2021","unstructured":"Wang R, Hernani-Morales C, Mart\u00edn-guerrero JD, Solano E, Albarr\u00e1n-arriagada F (2021) Quantum pattern recognition in photonic circuits. Quantum Sci Technol 7:015010","journal-title":"Quantum Sci Technol"},{"key":"88_CR62","doi-asserted-by":"publisher","first-page":"1845","DOI":"10.1109\/TIT.2017.2776228","volume":"64","author":"T Wiatowski","year":"2017","unstructured":"Wiatowski T, B\u00f6lcskei H (2017) A mathematical theory of deep convolutional neural networks for feature extraction. IEEE Trans Inf Theory 64:1845","journal-title":"IEEE Trans Inf Theory"},{"key":"88_CR63","unstructured":"Wilde MM (2011) From classical to quantum Shannon theory. arXiv:1106.1445"},{"key":"88_CR64","doi-asserted-by":"publisher","first-page":"043003","DOI":"10.1088\/1367-2630\/aa65de","volume":"19","author":"BP Williams","year":"2017","unstructured":"Williams BP, Lougovski P (2017) Quantum state estimation when qubits are lost: a no-data-left-behind approach. New J Phys 19:043003","journal-title":"New J Phys"},{"key":"88_CR65","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0003-4916(89)90322-9","volume":"191","author":"WK Wootters","year":"1989","unstructured":"Wootters WK, Fields BD (1989) Optimal state-determination by mutually unbiased measurements. Ann Phys 191:363","journal-title":"Ann Phys"},{"key":"88_CR66","doi-asserted-by":"crossref","unstructured":"Zia D, Checchinato R, Suprano A, Giordani T, Polino E, Innocenti L, Ferraro A, Paternostro M, Spagnoloand N, Sciarrino F (2022) Regression of high dimensional angular momentum states of light. arXiv:2206.09873","DOI":"10.1103\/PhysRevResearch.5.013142"},{"key":"88_CR67","doi-asserted-by":"publisher","first-page":"10115","DOI":"10.1088\/0305-4470\/36\/39\/310","volume":"36","author":"K Zyczkowski","year":"2003","unstructured":"Zyczkowski K, Sommers H-J (2003) Hilbert\u2013Schmidt volume of the set of mixed quantum states. J Phys A: Math Gen 36:10115","journal-title":"J Phys A: Math Gen"},{"key":"88_CR68","doi-asserted-by":"publisher","first-page":"032313","DOI":"10.1103\/PhysRevA.71.032313","volume":"71","author":"K Zyczkowski","year":"2005","unstructured":"Zyczkowski K, Sommers H-J (2005) Average fidelity between random quantum states. Phys Rev A 71:032313","journal-title":"Phys Rev A"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-022-00088-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-022-00088-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-022-00088-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T08:03:06Z","timestamp":1687161786000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-022-00088-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,26]]},"references-count":68,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["88"],"URL":"https:\/\/doi.org\/10.1007\/s42484-022-00088-8","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"type":"print","value":"2524-4906"},{"type":"electronic","value":"2524-4914"}],"subject":[],"published":{"date-parts":[[2022,12,26]]},"assertion":[{"value":"12 May 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 December 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}],"article-number":"1"}}