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In this work, we tackle the problem of such interplay in random pure quantum states. We show that while there is a strong dependence between entanglement and magic, they are, surprisingly, perfectly uncorrelated. We compute the expectation value of non-stabilizerness given the Schmidt spectrum (and thus entanglement). At a first approximation, entanglement determines the average magic on the Schmidt orbit. However, there is a finer structure in the average magic distinguishing different orbits where the flatness of entanglement spectrum is involved.<\/jats:p>","DOI":"10.22331\/q-2025-07-21-1797","type":"journal-article","created":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T11:17:12Z","timestamp":1753096632000},"page":"1797","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Entanglement and Stabilizer entropies of random bipartite pure quantum states"],"prefix":"10.22331","volume":"9","author":[{"given":"Daniele","family":"Iannotti","sequence":"first","affiliation":[{"name":"Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138 Napoli, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli"}]},{"given":"Gianluca","family":"Esposito","sequence":"additional","affiliation":[{"name":"Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138 Napoli, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli"}]},{"given":"Lorenzo","family":"Campos Venuti","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Napoli Federico II , Dipartimento di Fisica Ettore Pancini"},{"name":"Department of Physics and Astronomy, University of Southern California, Los Angeles, USA"}]},{"given":"Alioscia","family":"Hamma","sequence":"additional","affiliation":[{"name":"Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138 Napoli, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli"},{"name":"Universit\u00e0 degli Studi di Napoli Federico II , Dipartimento di Fisica Ettore Pancini"}]}],"member":"9598","published-online":{"date-parts":[[2025,7,21]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Ryszard Horodecki, Pawe\u0142 Horodecki, Micha\u0142 Horodecki, and Karol Horodecki. Quantum entanglement. 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