{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:32:28Z","timestamp":1760661148634,"version":"build-2065373602"},"reference-count":66,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T00:00:00Z","timestamp":1755734400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T00:00:00Z","timestamp":1755734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12235008"],"award-info":[{"award-number":["12235008"]}],"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"],"DOI":"10.1007\/s11128-025-04901-8","type":"journal-article","created":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T06:19:05Z","timestamp":1755757145000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A universal quantum certainty relation for arbitrary number of observables"],"prefix":"10.1007","volume":"24","author":[{"given":"Ao-Xiang","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ma-Cheng","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong-Feng","family":"Qiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,8,21]]},"reference":[{"key":"4901_CR1","doi-asserted-by":"crossref","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. Z. Phys. 43, 172\u2013198 (1927)","journal-title":"Z. Phys."},{"key":"4901_CR2","doi-asserted-by":"crossref","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\u2013164 (1929)","journal-title":"Phys. Rev."},{"key":"4901_CR3","first-page":"296","volume":"14","author":"E Schr\u00f6dinger","year":"1930","unstructured":"Schr\u00f6dinger, E.: Sitzungsberichte der Preussischen Akademie der Wissenschaften. Physikalisch-mathematische Klasse 14, 296 (1930)","journal-title":"Physikalisch-mathematische Klasse"},{"key":"4901_CR4","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1103\/RevModPhys.86.1261","volume":"86","author":"P Busch","year":"2014","unstructured":"Busch, P., Lahti, P., Werner, R.F.: Colloquium: Quantum root-mean-square error and measurement uncertainty relations. Rev. Mod. Phys. 86, 1261\u20131281 (2014)","journal-title":"Rev. Mod. Phys."},{"key":"4901_CR5","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.90.062118","volume":"90","author":"S Kechrimparis","year":"2014","unstructured":"Kechrimparis, S., Weigert, S.: Heisenberg uncertainty relation for three canonical observables. Phys. Rev. A 90, 062118 (2014)","journal-title":"Phys. Rev. A"},{"key":"4901_CR6","doi-asserted-by":"crossref","first-page":"14238","DOI":"10.1038\/srep14238","volume":"5","author":"B Chen","year":"2015","unstructured":"Chen, B., Fei, S.-M.: Sum uncertainty relations for arbitrary N incompatible observables. Sci. Rep. 5, 14238 (2015)","journal-title":"Sci. Rep."},{"key":"4901_CR7","doi-asserted-by":"crossref","first-page":"2925","DOI":"10.1016\/j.physleta.2016.06.054","volume":"380","author":"Q-C Song","year":"2016","unstructured":"Song, Q.-C., Qiao, C.-F.: Stronger Schr\u00f6dinger-like uncertainty relations. Phys. Lett. A 380, 2925\u20132930 (2016)","journal-title":"Phys. Lett. A"},{"key":"4901_CR8","doi-asserted-by":"crossref","first-page":"31192","DOI":"10.1038\/srep31192","volume":"6","author":"H-H Qin","year":"2016","unstructured":"Qin, H.-H., Fei, S.-M., Li-Jost, X.: Multi-observable uncertainty relations in product form of variances. Sci. Rep. 6, 31192 (2016)","journal-title":"Sci. Rep."},{"key":"4901_CR9","doi-asserted-by":"crossref","first-page":"44764","DOI":"10.1038\/srep44764","volume":"7","author":"QC Song","year":"2017","unstructured":"Song, Q.C., Li, J.L., Peng, G.X., Qiao, C.F.: A stronger multi-observable uncertainty relation. Sci. Rep. 7, 44764 (2017)","journal-title":"Sci. Rep."},{"key":"4901_CR10","volume":"108","author":"S Yu","year":"2023","unstructured":"Yu, S., Mao, Y.-L., Niu, C., Chen, H., Li, Z.-D., Fan, J.: Measurement uncertainty relation for three observables. Phys. Rev. A 108, 042208 (2023)","journal-title":"Phys. Rev. A"},{"key":"4901_CR11","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s11128-024-04544-1","volume":"23","author":"A-X Liu","year":"2024","unstructured":"Liu, A.-X., Yang, M.-C., Qiao, C.-F.: Quantum uncertainty equalities and inequalities for unitary operators. Quantum Inf. Process. 23, 333 (2024)","journal-title":"Quantum Inf. Process."},{"key":"4901_CR12","unstructured":"Abd-Rabbou, M.Y., Qiao, C.F.: Strengthening the uncertainty and the reverse uncertainty relation limits. arXiv preprint arXiv:2508.02036"},{"key":"4901_CR13","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1103\/RevModPhys.29.454","volume":"29","author":"H Everett","year":"1957","unstructured":"Everett, H.: \u201cRelative state\u2019\u2019 formulation of quantum mechanics. Rev. Mod. Phys. 29, 454\u2013462 (1957)","journal-title":"Rev. Mod. Phys."},{"key":"4901_CR14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF01608825","volume":"44","author":"I Bia\u0142ynicki-Birula","year":"1975","unstructured":"Bia\u0142ynicki-Birula, I., Mycielski, J.: Uncertainty relations for information entropy in wave mechanics. Commun. Math. Phys. 44, 129\u2013132 (1975)","journal-title":"Commun. Math. Phys."},{"key":"4901_CR15","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1103\/PhysRevLett.50.631","volume":"50","author":"D Deutsch","year":"1983","unstructured":"Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631\u2013633 (1983)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR16","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1103\/PhysRevLett.60.1103","volume":"60","author":"H Maassen","year":"1988","unstructured":"Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103\u20131106 (1988)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR17","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/12\/2\/025009","volume":"12","author":"S Wehner","year":"2010","unstructured":"Wehner, S., Winter, A.: Entropic uncertainty relations\u2014a survey. New J. Phys. 12, 025009 (2010)","journal-title":"New J. Phys."},{"key":"4901_CR18","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.108.210405","volume":"108","author":"PJ Coles","year":"2012","unstructured":"Coles, P.J., Colbeck, R., Yu, L., Zwolak, M.: Uncertainty relations from simple entropic properties. Phys. Rev. Lett. 108, 210405 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR19","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.physleta.2014.11.002","volume":"379","author":"PJ Coles","year":"2015","unstructured":"Coles, P.J., Furrer, F.: State-dependent approach to entropic measurement\u2014disturbance relations. Phys. Lett. A 379, 105\u2013112 (2015)","journal-title":"Phys. Lett. A"},{"key":"4901_CR20","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1002\/andp.201600130","volume":"528","author":"AE Rastegin","year":"2016","unstructured":"Rastegin, A.E.: Entropic uncertainty relations for successive measurements of canonically conjugate observables. Ann. Phys. 528, 835\u2013844 (2016)","journal-title":"Ann. Phys."},{"key":"4901_CR21","doi-asserted-by":"crossref","DOI":"10.1103\/RevModPhys.89.015002","volume":"89","author":"PJ Coles","year":"2017","unstructured":"Coles, P.J., Berta, M., Tomamichel, M., Wehner, S.: Entropic uncertainty relations and their applications. Rev. Mod. Phys. 89, 015002 (2017)","journal-title":"Rev. Mod. Phys."},{"key":"4901_CR22","first-page":"03LT01","volume":"50","author":"JL Li","year":"2016","unstructured":"Li, J.L., Qiao, C.F.: Equivalence theorem of uncertainty relations. J. Phys. A: Math. Theor. 50, 03LT01 (2016)","journal-title":"J. Phys. A: Math. Theor."},{"key":"4901_CR23","doi-asserted-by":"crossref","unstructured":"Marshall, A.W., Olkin, I., Arnold, B.C.: Inequalities: Theory of Majorization and Its Applications, vol. 143, 2nd edn. Springer, Berlin (2011)","DOI":"10.1007\/978-0-387-68276-1"},{"key":"4901_CR24","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.84.052117","volume":"84","author":"MH Partovi","year":"2011","unstructured":"Partovi, M.H.: Majorization formulation of uncertainty in quantum mechanics. Phys. Rev. A 84, 052117 (2011)","journal-title":"Phys. Rev. A"},{"key":"4901_CR25","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.111.230401","volume":"111","author":"S Friedland","year":"2013","unstructured":"Friedland, S., Gheorghiu, V., Gour, G.: Universal uncertainty relations. Phys. Rev. Lett. 111, 230401 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR26","doi-asserted-by":"crossref","DOI":"10.1088\/1751-8113\/46\/27\/272002","volume":"46","author":"Z Pucha\u0142a","year":"2013","unstructured":"Pucha\u0142a, Z., Rudnicki, \u0141, \u017byczkowski, K.: Majorization entropic uncertainty relations. J. Phys. A: Math. Theor. 46, 272002 (2013)","journal-title":"J. Phys. A: Math. Theor."},{"key":"4901_CR27","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/18\/3\/033019","volume":"18","author":"V Narasimhachar","year":"2016","unstructured":"Narasimhachar, V., Poostindouz, A., Gour, G.: Uncertainty, joint uncertainty, and the quantum uncertainty principle. New J. Phys. 18, 033019 (2016)","journal-title":"New J. Phys."},{"key":"4901_CR28","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.97.042130","volume":"97","author":"G Gour","year":"2018","unstructured":"Gour, G., Grudka, A., Horodecki, M., Klobus, W., Lodyga, J., Narasimhachar, V.: Conditional uncertainty principle. Phys. Rev. A 97, 042130 (2018)","journal-title":"Phys. Rev. A"},{"key":"4901_CR29","doi-asserted-by":"crossref","first-page":"1900143","DOI":"10.1002\/andp.201900143","volume":"531","author":"JL Li","year":"2019","unstructured":"Li, J.L., Qiao, C.F.: The optimal uncertainty relation. Ann. Phys. 531, 1900143 (2019)","journal-title":"Ann. Phys."},{"key":"4901_CR30","volume":"130","author":"Y Xiao","year":"2023","unstructured":"Xiao, Y., Yang, Y., Wang, X., Liu, Q., Gu, M.: Quantum uncertainty principles for measurements with interventions. Phys. Rev. Lett. 130, 240201 (2023)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR31","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1109\/18.992785","volume":"48","author":"F Cicalese","year":"2002","unstructured":"Cicalese, F., Vaccaro, U.: Supermodularity and subadditivity properties of the entropy on the majorization lattice. IEEE Trans. Inf. Theory 48, 933\u2013938 (2002)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"4901_CR32","doi-asserted-by":"crossref","DOI":"10.1016\/j.physleta.2022.128105","volume":"438","author":"S Wang","year":"2022","unstructured":"Wang, S., Meng, F.X., Wang, H., Qiao, C.F.: Experimental test of the majorization uncertainty relation with mixed states. Phys. Lett. A 438, 128105 (2022)","journal-title":"Phys. Lett. A"},{"key":"4901_CR33","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1007\/s11128-019-2530-0","volume":"19","author":"H Wang","year":"2020","unstructured":"Wang, H., Li, J.L., Wang, S., Song, Q.C., Qiao, C.F.: Experimental investigation of the uncertainty relations with coherent light. Quantum Inf. Process. 19, 38 (2020)","journal-title":"Quantum Inf. Process."},{"key":"4901_CR34","volume":"95","author":"D Mondal","year":"2017","unstructured":"Mondal, D., Bagchi, S., Pati, A.K.: Tighter uncertainty and reverse uncertainty relations. Phys. Rev. A 95, 052117 (2017)","journal-title":"Phys. Rev. A"},{"key":"4901_CR35","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevResearch.2.023106","volume":"2","author":"L Xiao","year":"2020","unstructured":"Xiao, L., Fan, B., Wang, K., Pati, A.K., Xue, P.: Direct experimental test of forward and reverse uncertainty relations. Phys. Rev. Res. 2, 023106 (2020)","journal-title":"Phys. Rev. Res."},{"key":"4901_CR36","volume":"89","author":"K Korzekwa","year":"2014","unstructured":"Korzekwa, K., Jennings, D., Rudolph, T.: Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations. Phys. Rev. A 89, 052108 (2014)","journal-title":"Phys. Rev. A"},{"key":"4901_CR37","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0375-9601(93)90269-6","volume":"173","author":"J S\u00e1nchez","year":"1993","unstructured":"S\u00e1nchez, J.: Entropic uncertainty and certainty relations for complementary observables. Phys. Lett. A 173, 233\u2013239 (1993)","journal-title":"Phys. Lett. A"},{"key":"4901_CR38","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0375-9601(95)00219-S","volume":"201","author":"J S\u00e1nchez-Ruiz","year":"1995","unstructured":"S\u00e1nchez-Ruiz, J.: Improved bounds in the entropic uncertainty and certainty relations for complementary observables. Phys. Lett. A 201, 125\u2013131 (1995)","journal-title":"Phys. Lett. A"},{"key":"4901_CR39","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1142\/S0219749910006502","volume":"08","author":"T Durt","year":"2010","unstructured":"Durt, T., Englert, B.G., Bengtsson, I., \u017byczkowski, K.: On mutually unbiased bases. Int. J. Quantum Inf. 08, 535\u2013640 (2010)","journal-title":"Int. J. Quantum Inf."},{"key":"4901_CR40","volume":"92","author":"Z Pucha\u0142a","year":"2015","unstructured":"Pucha\u0142a, Z., Rudnicki, \u0141, Chabuda, K., Paraniak, M., \u017byczkowski, K.: Certainty relations, mutual entanglement, and nondisplaceable manifolds. Phys. Rev. A 92, 032109 (2015)","journal-title":"Phys. Rev. A"},{"key":"4901_CR41","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2021.126275","volume":"582","author":"B Canturk","year":"2021","unstructured":"Canturk, B., Gedik, Z.: Optimal upper bound of entropic uncertainty relation for mutually unbiased bases. Phys. A 582, 126275 (2021)","journal-title":"Phys. A"},{"key":"4901_CR42","volume-title":"Quantum Computation and Quantum Information","author":"ILC Michael","year":"2010","unstructured":"Michael, I.L.C., Nielsen, A.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)"},{"key":"4901_CR43","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1103\/PhysRevLett.83.436","volume":"83","author":"MA Nielsen","year":"1999","unstructured":"Nielsen, M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436\u2013439 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR44","volume":"92","author":"Y Yao","year":"2015","unstructured":"Yao, Y., Xiao, X., Ge, L., Sun, C.P.: Quantum coherence in multipartite systems. Phys. Rev. A 92, 022112 (2015)","journal-title":"Phys. Rev. A"},{"key":"4901_CR45","volume":"91","author":"S Du","year":"2015","unstructured":"Du, S., Bai, Z., Guo, Y.: Conditions for coherence transformations under incoherent operations. Phys. Rev. A 91, 052120 (2015)","journal-title":"Phys. Rev. A"},{"key":"4901_CR46","volume":"93","author":"K Bu","year":"2016","unstructured":"Bu, K., Singh, U., Wu, J.: Catalytic coherence transformations. Phys. Rev. A 93, 042326 (2016)","journal-title":"Phys. Rev. A"},{"key":"4901_CR47","volume":"95","author":"S Du","year":"2017","unstructured":"Du, S., Bai, Z., Guo, Y.: Erratum: Conditions for coherence transformations under incoherent operations [Phys. Rev. A 91, 052120 (2015)]. Phys. Rev. A 95, 029901 (2017)","journal-title":"Phys. Rev. A"},{"key":"4901_CR48","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.physa.2016.12.083","volume":"473","author":"GM Bosyk","year":"2017","unstructured":"Bosyk, G.M., Sergioli, G., Freytes, H., Holik, F., Bellomo, G.: Approximate transformations of bipartite pure-state entanglement from the majorization lattice. Phys. A 473, 403\u2013411 (2017)","journal-title":"Phys. A"},{"key":"4901_CR49","volume":"123","author":"CL Liu","year":"2019","unstructured":"Liu, C.L., Zhou, D.L.: Deterministic coherence distillation. Phys. Rev. Lett. 123, 070402 (2019)","journal-title":"Phys. Rev. Lett."},{"key":"4901_CR50","volume":"554","author":"A-X Liu","year":"2025","unstructured":"Liu, A.-X., Qiao, C.-F.: Probabilistic coherence transformation under strictly incoherent operation. Phys. Lett. A 554, 130739 (2025)","journal-title":"Phys. Lett. A"},{"key":"4901_CR51","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.70.022316","volume":"70","author":"O G\u00fchne","year":"2004","unstructured":"G\u00fchne, O., Lewenstein, M.: Entropic uncertainty relations and entanglement. Phys. Rev. A 70, 022316 (2004)","journal-title":"Phys. Rev. A"},{"key":"4901_CR52","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.86.022309","volume":"86","author":"MH Partovi","year":"2012","unstructured":"Partovi, M.H.: Entanglement detection using majorization uncertainty bounds. Phys. Rev. A 86, 022309 (2012)","journal-title":"Phys. Rev. A"},{"key":"4901_CR53","volume":"96","author":"Z-A Jia","year":"2017","unstructured":"Jia, Z.-A., Wu, Y.-C., Guo, G.-C.: Characterizing nonlocal correlations via universal uncertainty relations. Phys. Rev. A 96, 032122 (2017)","journal-title":"Phys. Rev. A"},{"key":"4901_CR54","doi-asserted-by":"crossref","first-page":"2000039","DOI":"10.1002\/qute.202000039","volume":"3","author":"JL Li","year":"2020","unstructured":"Li, J.L., Qiao, C.F.: An optimal measurement strategy to beat the quantum uncertainty in correlated system. Adv. Quantum Technol. 3, 2000039 (2020)","journal-title":"Adv. Quantum Technol."},{"key":"4901_CR55","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s11128-021-03043-x","volume":"20","author":"JL Li","year":"2021","unstructured":"Li, J.L., Qiao, C.F.: Characterizing quantum nonlocalities per uncertainty relation. Quantum Inf. Process. 20, 109 (2021)","journal-title":"Quantum Inf. Process."},{"key":"4901_CR56","doi-asserted-by":"crossref","first-page":"L050202","DOI":"10.1103\/PhysRevA.108.L050202","volume":"108","author":"G Zhu","year":"2023","unstructured":"Zhu, G., Liu, A., Xiao, L., Wang, K., Qu, D., Li, J., Qiao, C., Xue, P.: Experimental investigation of conditional majorization uncertainty relations in the presence of quantum memory. Phys. Rev. A 108, L050202 (2023)","journal-title":"Phys. Rev. A"},{"key":"4901_CR57","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1007\/s11128-023-04003-3","volume":"22","author":"M-C Yang","year":"2023","unstructured":"Yang, M.-C., Li, J.-L., Qiao, C.-F.: An effective way of characterizing the quantum nonlocality. Quantum Inf. Process. 22, 242 (2023)","journal-title":"Quantum Inf. Process."},{"key":"4901_CR58","unstructured":"Yang, M.C., Qiao, C.F.: Witness the high-dimensional quantum steering via majorization lattice. arXiv preprint arXiv:2507.20950"},{"key":"4901_CR59","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0024-3795(91)90287-7","volume":"145","author":"RB Bapat","year":"1991","unstructured":"Bapat, R.B.: Majorization and singular values. III. Linear Algebra Appl. 145, 59\u201370 (1991)","journal-title":"Linear Algebra Appl."},{"key":"4901_CR60","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0024-3795(94)90344-1","volume":"199","author":"JV Bondar","year":"1994","unstructured":"Bondar, J.V.: Inequalities: theory of majorization and its applications: by Albert W. Marshall and Ingram Olkin. Linear Algebra Appl. 199, 115\u2013130 (1994)","journal-title":"Linear Algebra Appl."},{"key":"4901_CR61","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/ab3734","volume":"21","author":"GM Bosyk","year":"2019","unstructured":"Bosyk, G.M., Bellomo, G., Holik, F., Freytes, H., Sergioli, G.: Optimal common resource in majorization-based resource theories. New J. Phys. 21, 083028 (2019)","journal-title":"New J. Phys."},{"key":"4901_CR62","first-page":"209","volume":"9","author":"MO Lorenz","year":"1905","unstructured":"Lorenz, M.O.: Methods of measuring the concentration of wealth. Publ. Am. Stat. Assoc. 9, 209\u2013219 (1905)","journal-title":"Publ. Am. Stat. Assoc."},{"key":"4901_CR63","doi-asserted-by":"crossref","first-page":"2220","DOI":"10.1109\/TIT.2017.2787181","volume":"64","author":"F Cicalese","year":"2018","unstructured":"Cicalese, F., Gargano, L., Vaccaro, U.: Bounds on the entropy of a function of a random variable and their applications. IEEE Trans. Inf. Theory 64, 2220\u20132230 (2018)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"4901_CR64","volume":"96","author":"S Luo","year":"2017","unstructured":"Luo, S., Sun, Y.: Quantum coherence versus quantum uncertainty. Phys. Rev. A 96, 022130 (2017)","journal-title":"Phys. Rev. A"},{"key":"4901_CR65","volume":"103","author":"Y Sun","year":"2021","unstructured":"Sun, Y., Luo, S.: Coherence as uncertainty. Phys. Rev. A 103, 042423 (2021)","journal-title":"Phys. Rev. A"},{"key":"4901_CR66","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.103.012403","volume":"103","author":"GM Bosyk","year":"2021","unstructured":"Bosyk, G.M., Losada, M., Massri, C., Freytes, H., Sergioli, G.: Generalized coherence vector applied to coherence transformations and quantifiers. Phys. Rev. A 103, 012403 (2021)","journal-title":"Phys. Rev. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04901-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04901-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04901-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T17:40:27Z","timestamp":1760636427000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04901-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,21]]},"references-count":66,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["4901"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04901-8","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2025,8,21]]},"assertion":[{"value":"15 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 August 2025","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 conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"278"}}