{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T06:43:49Z","timestamp":1778654629969,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,25]],"date-time":"2022-04-25T00:00:00Z","timestamp":1650844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology","doi-asserted-by":"publisher","award":["MOST 110-2123-M-007-002, 110-2627-M-008-001"],"award-info":[{"award-number":["MOST 110-2123-M-007-002, 110-2627-M-008-001"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the International Technology Center 251 Indo-Pacific (ITC IPAC) and Army Research Office","award":["FA5209-21-P-0158"],"award-info":[{"award-number":["FA5209-21-P-0158"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the power to find the best fit to arbitrarily complicated symmetry, machine-learning (ML)-enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. Instead of using the reconstruction model in training a truncated density matrix, we develop a high-performance, lightweight, and easy-to-install supervised characteristic model by generating the target parameters directly. Such a characteristic model-based ML-QST can avoid the problem of dealing with a large Hilbert space, but cab keep feature extractions with high precision, capturing the underlying symmetry in data. With the experimentally measured data generated from the balanced homodyne detectors, we compare the degradation information about quantum noise squeezed states predicted by the reconstruction and characteristic models; both are in agreement with the empirically fitting curves obtained from the covariance method. Such a ML-QST with direct parameter estimations illustrates a crucial diagnostic toolbox for applications with squeezed states, from quantum information process, quantum metrology, advanced gravitational wave detectors, to macroscopic quantum state generation.<\/jats:p>","DOI":"10.3390\/sym14050874","type":"journal-article","created":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T02:14:39Z","timestamp":1650939279000},"page":"874","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Direct Parameter Estimations from Machine Learning-Enhanced Quantum State Tomography"],"prefix":"10.3390","volume":"14","author":[{"given":"Hsien-Yi","family":"Hsieh","sequence":"first","affiliation":[{"name":"Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingyu","family":"Ning","sequence":"additional","affiliation":[{"name":"Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8580-9025","authenticated-orcid":false,"given":"Yi-Ru","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hsun-Chung","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hua Li","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3191-8845","authenticated-orcid":false,"given":"Chien-Ming","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7171-7274","authenticated-orcid":false,"given":"Ray-Kuang","family":"Lee","sequence":"additional","affiliation":[{"name":"Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan"},{"name":"Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan"},{"name":"Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan"},{"name":"Center for Quantum Technology, Hsinchu 30013, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R1561","DOI":"10.1103\/PhysRevA.55.R1561","article-title":"Quantum-state estimation","volume":"55","author":"Hradil","year":"1997","journal-title":"Phys. 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