{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:58:52Z","timestamp":1760241532976,"version":"build-2065373602"},"reference-count":88,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,19]],"date-time":"2018-04-19T00:00:00Z","timestamp":1524096000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Stern\u2013Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations    C ( z , \u03b8 )    by redefining the Banaszek\u2013W\u00f3dkiewicz correlation in terms of the Wigner operator, that is    C  ( z , \u03b8 )  =  \u27e8 \u03a8 |  W ^   ( z ,  p z  )   \u03c3 ^   ( \u03b8 )   | \u03a8 \u27e9    , where     W ^   ( z ,  p z  )     is the Wigner operator,     \u03c3 ^   ( \u03b8 )     is the Pauli spin operator in an arbitrary direction   \u03b8   and    | \u03a8 \u27e9    is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser\u2013Horne\u2013Shimony\u2013Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.<\/jats:p>","DOI":"10.3390\/e20040299","type":"journal-article","created":{"date-parts":[[2018,4,20]],"date-time":"2018-04-20T04:24:21Z","timestamp":1524198261000},"page":"299","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Quantum Nonlocality and Quantum Correlations in the Stern\u2013Gerlach Experiment"],"prefix":"10.3390","volume":"20","author":[{"given":"Alma Elena","family":"Piceno Mart\u00ednez","sequence":"first","affiliation":[{"name":"Facultad de Ciencias F\u00edsico Matem\u00e1ticas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, 18 Sur y Avenida San Claudio, Col. San Manuel, Puebla 72520, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernesto","family":"Ben\u00edtez Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias F\u00edsico Matem\u00e1ticas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, 18 Sur y Avenida San Claudio, Col. San Manuel, Puebla 72520, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julio Abraham","family":"Mendoza Fierro","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias F\u00edsico Matem\u00e1ticas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, 18 Sur y Avenida San Claudio, Col. San Manuel, Puebla 72520, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcela Maribel","family":"M\u00e9ndez Otero","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias F\u00edsico Matem\u00e1ticas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, 18 Sur y Avenida San Claudio, Col. San Manuel, Puebla 72520, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7603-3667","authenticated-orcid":false,"given":"Luis Manuel","family":"Ar\u00e9valo Aguilar","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias F\u00edsico Matem\u00e1ticas, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, 18 Sur y Avenida San Claudio, Col. San Manuel, Puebla 72520, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,19]]},"reference":[{"key":"ref_1","first-page":"165","article-title":"Space Quantization: Otto Stern\u2019s Lucky Star","volume":"127","author":"Friedrich","year":"1998","journal-title":"Daedalus"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1063\/1.1650229","article-title":"Stern and Gerlach: How a bad cigar helped reorient atomic physics","volume":"56","author":"Friedrich","year":"2003","journal-title":"Phys. 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