{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:35:57Z","timestamp":1760060157439,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T00:00:00Z","timestamp":1754265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Smart Grid-National Science and Technology Major Project","award":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"],"award-info":[{"award-number":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"]}]},{"name":"National Natural Science Foundation of China","award":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"],"award-info":[{"award-number":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"]}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"publisher","award":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"],"award-info":[{"award-number":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project of Cultivation for Young top-notch Talents of Beijing Municipal Institutions","award":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"],"award-info":[{"award-number":["2024ZD0801900","11505125","12175002","11705004","12381240288","1222020","BPHR202203034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we introduce a novel method to extract correlations in diagonal quantum states in multi-particle quantum systems, addressing a significant limitation of traditional approaches that require prior knowledge of the density matrices of quantum states. Instead of relying on classical information processing, our method is based on weak couplings and ancillary systems, eliminating the need for classical communication, optimization, and complex calculations. The concept of mutually unbiased bases is intrinsically linked to symmetry, as it entails the uniform distribution of quantum states across distinct bases. Within the framework of our theoretical model, mutually unbiased bases are employed to facilitate weak measurements and to function as the post-selected states. To quantify the correlations in the initial state, we employ the trace distance between the initial state and the product of its marginal states, and illustrate the feasibility and effectiveness of our approach. We generalize the approach to accommodate high-dimensional multi-particle systems for potential applications in quantum information processing and quantum networks.<\/jats:p>","DOI":"10.3390\/sym17081233","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T11:54:51Z","timestamp":1754308491000},"page":"1233","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extracting Correlations in Arbitrary Diagonal Quantum States via Weak Couplings and Auxiliary Systems"],"prefix":"10.3390","volume":"17","author":[{"given":"Hui","family":"Li","sequence":"first","affiliation":[{"name":"Integrated Circuit College, Beijing Polytechnic University, Beijing 100176, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8942-6651","authenticated-orcid":false,"given":"Chao","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Energy Storage Science and Engineering, North China University of Technology, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yansong","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7888-055X","authenticated-orcid":false,"given":"Xian","family":"Lu","sequence":"additional","affiliation":[{"name":"China Mobile Research Institute, Beijing 100053, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1103\/PhysRevLett.60.1351","article-title":"How the Result of a Measurement of a Component of the Spin of a Spin-1\/2 Particle Can Turn Out to be 100","volume":"60","author":"Aharonov","year":"1988","journal-title":"Phys. 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