{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:53:37Z","timestamp":1760241217708,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T00:00:00Z","timestamp":1577059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001868","name":"National Science Council","doi-asserted-by":"publisher","award":["102-2112-M-033-003","107-2112-M-033-008","108-2112-M-033-003"],"award-info":[{"award-number":["102-2112-M-033-003","107-2112-M-033-008","108-2112-M-033-003"]}],"id":[{"id":"10.13039\/501100001868","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein\u2013Podolsky\u2013Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.<\/jats:p>","DOI":"10.3390\/e22010019","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:15:01Z","timestamp":1577070901000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Exploring Multipartite Steering Effect Using Bell Operators"],"prefix":"10.3390","volume":"22","author":[{"given":"Li-Yi","family":"Hsu","sequence":"first","affiliation":[{"name":"Department of Physics, Chung Yuan Christian University, Chungli 32081, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4237-8784","authenticated-orcid":false,"given":"Shoichi","family":"Kawamoto","sequence":"additional","affiliation":[{"name":"Department of Physics, Chung Yuan Christian University, Chungli 32081, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"032112","DOI":"10.1103\/PhysRevA.80.032112","article-title":"Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox","volume":"80","author":"Cavalcanti","year":"2009","journal-title":"Phys. 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Lett."},{"key":"ref_41","unstructured":"Here the observable pair M10 and M11 are said most incompatible since they each are projective measurements onto mutually unbiased bases."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"10002","DOI":"10.1209\/0295-5075\/103\/10002","article-title":"Comparing the degrees of incompatibility inherent in probabilistic physical theories","volume":"103","author":"Busch","year":"2013","journal-title":"Eur. Phys. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"230402","DOI":"10.1103\/PhysRevLett.115.230402","article-title":"One-to-one mapping between steering and joint measurability problems","volume":"115","author":"Uola","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"052105","DOI":"10.1103\/PhysRevA.95.052105","article-title":"N-term pairwise-correlation inequalities, steering, and joint measurability","volume":"95","author":"Karthik","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_45","unstructured":"We can construct alernative task functions based on (1), (2), (3), and (4). For example, we can put down H=12\u2211i=01\u2211B=Bk,Bk\u2032B(Bn\u2212k+(\u22121)iBn\u2212k\u2032)2 and I=12\u2211B=Bn\u2212k,Bn\u2212k\u2032\u2211i=01(Bk+(\u22121)iBk\u2032)B2. Wherein, the steering effect of both Bk and Bk\u2032 ((Bk+Bk\u2032) and (Bk\u2212Bk\u2032)) on the Bn\u2212k+Bn\u2212k\u2032 and Bn\u2212k\u2212Bn\u2212k\u2032 (Bn\u2212k and Bn\u2212k\u2032) are evalauted in each square root terms in the fucntion H (I). In the LHV\u2013LHS model, we have HV\u2212S\u2264max\u03c1\u03bb{Bn\u2212kLHS,Bn\u2212k\u2032LHS} and IV\u2212S\u2264max\u03c1\u03bb{Bn\u2212kLHS+Bn\u2212k\u2032LHS}. Notably, as for the Bell operators, BnV\u2212\u2212S, Bn\u2032LHVV\u2212\u2212S each have the same upper bound as HV\u2212S."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"020103","DOI":"10.1103\/PhysRevA.93.020103","article-title":"Quantification of Einstein-Podolski-Rosen steering for two-qubit states","volume":"93","author":"Costa","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"093006","DOI":"10.1088\/1367-2630\/aadc78","article-title":"Geometric extension of Clauser-Horne inequality to more qubits","volume":"20","author":"Dutta","year":"2018","journal-title":"New J. of Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"042123","DOI":"10.1103\/PhysRevA.95.042123","article-title":"Mermin inequalities for perfect correlations in many-qutrit systems","volume":"95","author":"Lawrence","year":"2017","journal-title":"Phys. Rev. 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A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:44:48Z","timestamp":1760190288000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,23]]},"references-count":53,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["e22010019"],"URL":"https:\/\/doi.org\/10.3390\/e22010019","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,12,23]]}}}