{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T15:15:00Z","timestamp":1760800500488,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T00:00:00Z","timestamp":1635206400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T00:00:00Z","timestamp":1635206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971140","61771174"],"award-info":[{"award-number":["11971140","61771174"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12075159"],"award-info":[{"award-number":["12075159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s11128-021-03303-w","type":"journal-article","created":{"date-parts":[[2021,10,26]],"date-time":"2021-10-26T08:05:47Z","timestamp":1635235547000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Uncertainty regions of observables and state-independent uncertainty relations"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6220-4218","authenticated-orcid":false,"given":"Lin","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Shunlong","family":"Luo","sequence":"additional","affiliation":[]},{"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[]},{"given":"Junde","family":"Wu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,26]]},"reference":[{"key":"3303_CR1","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/BF01397280","volume":"43","author":"W Heisenberg","year":"1927","unstructured":"Heisenberg, W.: \u00dcber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift f\u00fcr Physik 43, 172 (1927). https:\/\/doi.org\/10.1007\/BF01397280","journal-title":"Zeitschrift f\u00fcr Physik"},{"key":"3303_CR2","doi-asserted-by":"publisher","first-page":"093046","DOI":"10.1088\/1367-2630\/17\/9\/093046","volume":"17","author":"L Dammeier","year":"2015","unstructured":"Dammeier, L., Schwonneck, R., Werner, R.F.: Uncertainty relations for angular momentum. New J. Phys. 17, 093046 (2015). https:\/\/doi.org\/10.1088\/1367-2630\/17\/9\/093046","journal-title":"New J. Phys."},{"key":"3303_CR3","doi-asserted-by":"publisher","first-page":"12708","DOI":"10.1038\/srep12708","volume":"5","author":"JL Li","year":"2015","unstructured":"Li, J.L., Qiao, C.F.: Reformulating the quantum uncertainty relation. Sci. Rep. 5, 12708 (2015). https:\/\/doi.org\/10.1038\/srep12708","journal-title":"Sci. Rep."},{"key":"3303_CR4","doi-asserted-by":"publisher","first-page":"042121","DOI":"10.1103\/PhysRevA.98.042121","volume":"98","author":"H de Guise","year":"2018","unstructured":"de Guise, H., Maccone, L., Sanders, B.C., Shukla, N.: State-independent uncertainty relations. Phys. Rev. A 98, 042121 (2018). https:\/\/doi.org\/10.1103\/PhysRevA.98.042121","journal-title":"Phys. Rev. A"},{"key":"3303_CR5","doi-asserted-by":"publisher","first-page":"052121","DOI":"10.1103\/PhysRevA.99.052121","volume":"99","author":"P Giorda","year":"2019","unstructured":"Giorda, P., Maccone, L., Riccardi, A.: State-independent uncertainty relations from eigenvalue minimization. Phys. Rev. A 99, 052121 (2019). https:\/\/doi.org\/10.1103\/PhysRevA.99.052121","journal-title":"Phys. Rev. A"},{"key":"3303_CR6","doi-asserted-by":"publisher","first-page":"032118","DOI":"10.1103\/PhysRevA.100.032118","volume":"100","author":"Y Xiao","year":"2019","unstructured":"Xiao, Y., Guo, C., Meng, F., Jing, N., Yung, M.-H.: Incompatibility of observables as state-independent bound of uncertainty relations. Phys. Rev. A 100, 032118 (2019). https:\/\/doi.org\/10.1103\/PhysRevA.100.032118","journal-title":"Phys. Rev. A"},{"key":"3303_CR7","doi-asserted-by":"publisher","first-page":"042204","DOI":"10.1103\/PhysRevA.102.042204","volume":"102","author":"S Sponar","year":"2020","unstructured":"Sponar, S., Danner, A., Obigane, K., Hack, S., Hasegawa, Y.: Experimental test of tight state-independent preparation uncertainty relations for qubits. Phys. Rev. A 102, 042204 (2020). https:\/\/doi.org\/10.1103\/PhysRevA.102.042204","journal-title":"Phys. Rev. A"},{"key":"3303_CR8","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1126\/science.309.5731.98","volume":"309","author":"C Seife","year":"2005","unstructured":"Seife, C.: Do deeper principles underlie quantum uncertainty and nonlocality? Science 309, 98 (2005). https:\/\/doi.org\/10.1126\/science.309.5731.98","journal-title":"Science"},{"key":"3303_CR9","doi-asserted-by":"publisher","first-page":"032103","DOI":"10.1103\/PhysRevA.68.032103","volume":"68","author":"HF Hofmann","year":"2003","unstructured":"Hofmann, H.F., Takeuchi, S.: Violation of local uncertainty relations as a signature of entanglement. Phys. Rev. A 68, 032103 (2003). https:\/\/doi.org\/10.1103\/PhysRevA.68.032103","journal-title":"Phys. Rev. A"},{"key":"3303_CR10","doi-asserted-by":"publisher","first-page":"117903","DOI":"10.1103\/PhysRevLett.92.117903","volume":"92","author":"O G\u00fchne","year":"2004","unstructured":"G\u00fchne, O.: Characterizing entanglement via uncertainty relations. Phys. Rev. Lett. 92, 117903 (2004). https:\/\/doi.org\/10.1103\/PhysRevLett.92.117903","journal-title":"Phys. Rev. Lett."},{"key":"3303_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2009.02.004","volume":"474","author":"O G\u00fchne","year":"2009","unstructured":"G\u00fchne, O., T\u00f3th, G.: Entanglement detection. Phys. Rep. 474, 1 (2009). https:\/\/doi.org\/10.1016\/j.physrep.2009.02.004","journal-title":"Phys. Rep."},{"key":"3303_CR12","doi-asserted-by":"publisher","first-page":"170404","DOI":"10.1103\/PhysRevLett.119.170404","volume":"119","author":"R Schwonnek","year":"2017","unstructured":"Schwonnek, R., Dammeier, L., Werner, R.F.: State-independent uncertainty relations and entanglement detection in noisy systems. Phys. Rev. Lett. 119, 170404 (2017). https:\/\/doi.org\/10.1103\/PhysRevLett.119.170404","journal-title":"Phys. Rev. Lett."},{"key":"3303_CR13","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/s11128-018-1855-4","volume":"17","author":"C Qian","year":"2018","unstructured":"Qian, C., Li, J.-L., Qiao, C.-F.: State-independent uncertainty relations and entanglement detection. Quant. Inf. Process. 17, 84 (2018). https:\/\/doi.org\/10.1007\/s11128-018-1855-4","journal-title":"Quant. Inf. Process."},{"key":"3303_CR14","doi-asserted-by":"publisher","first-page":"220401","DOI":"10.1103\/PhysRevLett.122.220401","volume":"122","author":"Y-Y Zhao","year":"2019","unstructured":"Zhao, Y.-Y., Xiang, G.Y., Hu, X.M., Liu, B.H., Li, C.F., Guo, G.C., Schwonnek, R., Wolf, R.: Entanglement detection by violations of noisy uncertainty relations: a proof of principle. Phys. Rev. Lett. 122, 220401 (2019). https:\/\/doi.org\/10.1103\/PhysRevLett.122.220401","journal-title":"Phys. Rev. Lett."},{"key":"3303_CR15","doi-asserted-by":"publisher","first-page":"1072","DOI":"10.1126\/science.1192065","volume":"330","author":"J Oppenheim","year":"2010","unstructured":"Oppenheim, J., Wehner, S.: The uncertainty principle determines the nonlocality of quantum mechanics. Science 330, 1072\u20131074 (2010). https:\/\/doi.org\/10.1126\/science.1192065","journal-title":"Science"},{"key":"3303_CR16","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/BF01391200","volume":"44","author":"EH Kennard","year":"1927","unstructured":"Kennard, E.H.: Zur Quantenmechanik einfacher Bewegungstypen. Zeitschrift f\u00fcr Physik 44, 326 (1927). https:\/\/doi.org\/10.1007\/BF01391200","journal-title":"Zeitschrift f\u00fcr Physik"},{"key":"3303_CR17","volume-title":"Gruppentheorie und Quantenmechanik","author":"H Weyl","year":"1928","unstructured":"Weyl, H.: Gruppentheorie und Quantenmechanik. Hirzel, Leipzig (1928)"},{"key":"3303_CR18","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1103\/PhysRev.34.163","volume":"34","author":"HP Robertson","year":"1929","unstructured":"Robertson, H.P.: The uncertainty principle. Phys. Rev. 34, 163 (1929). https:\/\/doi.org\/10.1103\/PhysRev.34.163","journal-title":"Phys. Rev."},{"key":"3303_CR19","first-page":"296","volume":"14","author":"E Schr\u00f6dinger","year":"1930","unstructured":"Schr\u00f6dinger, E.: Zum Heisenbergschen Unscharfeprinzip. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse 14, 296 (1930)","journal-title":"Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse"},{"key":"3303_CR20","unstructured":"Busch, P., Reardon-Smith, O.: On quantum uncertainty relations and uncertainty regions. arXiv:1901.03695"},{"key":"3303_CR21","unstructured":"Vasudevrao, S., Sudha, I.R., Usha Devi, A.R., Rajagopal, A.K.: Sum uncertainty relations: uncertainty regions for qubits and qutrits. arXiv: 2101.11545v1"},{"key":"3303_CR22","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1063\/1.523763","volume":"19","author":"E Lubkin","year":"1978","unstructured":"Lubkin, E.: Entropy of an $$n$$-system from its correlation with a $$k$$-reservoir. J. Math. Phys. 19, 1028 (1978). https:\/\/doi.org\/10.1063\/1.523763","journal-title":"J. Math. Phys."},{"key":"3303_CR23","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1103\/PhysRevLett.71.1291","volume":"71","author":"DN Page","year":"1993","unstructured":"Page, D.N.: Average entropy of a subsystem. Phys. Rev. Lett. 71, 1291 (1993). https:\/\/doi.org\/10.1103\/PhysRevLett.71.1291","journal-title":"Phys. Rev. Lett."},{"key":"3303_CR24","doi-asserted-by":"publisher","unstructured":"Foong, S.K., Kanno, S.: Proof of Page\u2019s conjecture on the average entropy of a subsystem. Phys. Rev. Lett. 72, 1148 (1994). https:\/\/doi.org\/10.1103\/PhysRevLett.72.1148","DOI":"10.1103\/PhysRevLett.72.1148"},{"key":"3303_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRevLett.71.1291","volume":"77","author":"S Sen","year":"1996","unstructured":"Sen, S.: Average entropy of a quantum subsystem. Phys. Rev. Lett. 77, 1 (1996). https:\/\/doi.org\/10.1103\/PhysRevLett.71.1291","journal-title":"Phys. Rev. Lett."},{"key":"3303_CR26","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1038\/nphys1224","volume":"5","author":"MB Hastings","year":"2009","unstructured":"Hastings, M.B.: Superadditivity of communication capacity using entangled inputs. Nat. Phys. 5, 255 (2009). https:\/\/doi.org\/10.1038\/nphys1224","journal-title":"Nat. Phys."},{"key":"3303_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00220-014-2144-4","volume":"332","author":"M Christandl","year":"2014","unstructured":"Christandl, M., Doran, B., Kousidis, S., Walter, M.: Eigenvalue distributions of reduced density matrices. Commun. Math. Phys. 332, 1 (2014). https:\/\/doi.org\/10.1007\/s00220-014-2144-4","journal-title":"Commun. Math. Phys."},{"key":"3303_CR28","doi-asserted-by":"publisher","first-page":"2050010","DOI":"10.1142\/s2010326320500100","volume":"9","author":"S Dartois","year":"2020","unstructured":"Dartois, S., Lionni, L., Nechita, I.: The joint distribution of the marginals of multipartite random quantum states. Random Matrices Theory Appl. 9, 2050010 (2020). https:\/\/doi.org\/10.1142\/s2010326320500100","journal-title":"Random Matrices Theory Appl."},{"key":"3303_CR29","doi-asserted-by":"publisher","first-page":"1516","DOI":"10.1016\/j.physleta.2018.04.018","volume":"382","author":"L Zhang","year":"2018","unstructured":"Zhang, L., Wang, J., Chen, Z.H.: Spectral density of mixtures of random density matrices for qubits. Phys. Lett. A 382, 1516 (2018). https:\/\/doi.org\/10.1016\/j.physleta.2018.04.018","journal-title":"Phys. Lett. A"},{"key":"3303_CR30","doi-asserted-by":"publisher","first-page":"495203","DOI":"10.1088\/1751-8121\/ab5297","volume":"52","author":"L Zhang","year":"2019","unstructured":"Zhang, L., Jiang, Y.X., Wu, J.D.: Duistermaat\u2013Heckman measure and the mixture of quantum states. J. Phys. A Math. Theor. 52, 495203 (2019). https:\/\/doi.org\/10.1088\/1751-8121\/ab5297","journal-title":"J. Phys. A Math. Theor."},{"key":"3303_CR31","doi-asserted-by":"publisher","first-page":"1854","DOI":"10.1016\/j.physleta.2013.05.041","volume":"377","author":"LC Venuti","year":"2013","unstructured":"Venuti, L.C., Zanardi, P.: Probability density of quantum expectation values. Phys. Lett. A 377, 1854 (2013). https:\/\/doi.org\/10.1016\/j.physleta.2013.05.041","journal-title":"Phys. Lett. A"},{"key":"3303_CR32","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1063\/1.524438","volume":"21","author":"C Itzykson","year":"1980","unstructured":"Itzykson, C., Z\u00fcber, J.B.: The planar approximation. II. J. Math. Phys. 21, 411 (1980). https:\/\/doi.org\/10.1063\/1.524438","journal-title":"J. Math. Phys."},{"key":"3303_CR33","doi-asserted-by":"publisher","first-page":"7111","DOI":"10.1088\/0305-4470\/34\/35\/335","volume":"34","author":"K \u017byczkowski","year":"2001","unstructured":"\u017byczkowski, K., Sommers, H.-J.: Induced measures in the space of mixed quantum states. J. Phys. A Math. Theor. 34, 7111\u20137125 (2001). https:\/\/doi.org\/10.1088\/0305-4470\/34\/35\/335","journal-title":"J. Phys. A Math. Theor."},{"key":"3303_CR34","doi-asserted-by":"publisher","unstructured":"Zhang, L.: Dirac delta function of matrix argument. Int. J. Theor. Phys. (2020). https:\/\/doi.org\/10.1007\/s10773-020-04598-8","DOI":"10.1007\/s10773-020-04598-8"},{"key":"3303_CR35","doi-asserted-by":"publisher","first-page":"062139","DOI":"10.1103\/PhysRevE.100.062139","volume":"100","author":"L Zhang","year":"2019","unstructured":"Zhang, L., Xiang, H., Li-Jost, X., Fei, S.M.: Incompatibility probability of random quantum measurements. Phys. Rev. E 100, 062139 (2019). https:\/\/doi.org\/10.1103\/PhysRevE.100.062139","journal-title":"Phys. Rev. E"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03303-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03303-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03303-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T20:10:53Z","timestamp":1637698253000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03303-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,26]]},"references-count":35,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["3303"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03303-w","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2021,10,26]]},"assertion":[{"value":"27 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"357"}}