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In contrast to previous theoretical and experimental proposals the test requires three settings for the parties <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>A<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>C<\/mml:mi><\/mml:math>, but also six settings for the middle party <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>B<\/mml:mi><\/mml:math>, assuming separability of the sources. The bound we found for this symmetric configuration imposed on a real theory is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>14.69<\/mml:mn><\/mml:math> while the complex maximum is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>18<\/mml:mn><\/mml:math>. This large theoretical difference enables us to demonstrate the concomitant experimental violation on IBM quantum computer via a designed quantum network, without resorting to error mitigation, obtaining as a result <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>15.44<\/mml:mn><\/mml:math> at more than <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>100<\/mml:mn><\/mml:math> standard deviations above the found real bound.<\/jats:p>","DOI":"10.22331\/q-2025-01-15-1595","type":"journal-article","created":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T09:03:11Z","timestamp":1736931791000},"page":"1595","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Efficient discrimination between real and complex quantum theories"],"prefix":"10.22331","volume":"9","author":[{"given":"Josep","family":"Batle","sequence":"first","affiliation":[{"name":"Departament de F\u00edsica UIB i Institut d&apos;Aplicacions Computacionals de Codi Comunitari (IAC3), Campus UIB, E-07122 Palma de Mallorca, Balearic Islands, Spain"},{"name":"CRISP - Centre de Recerca Independent de sa Pobla, 07420 sa Pobla, Balearic Islands, Spain"}]},{"given":"Tomasz","family":"Bia\u0142ecki","sequence":"additional","affiliation":[{"name":"Faculty of Physics, University of Warsaw, ul. 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