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If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., e<\/mml:mi>n<\/mml:mi>t<\/mml:mi>a<\/mml:mi>n<\/mml:mi>g<\/mml:mi>l<\/mml:mi>e<\/mml:mi>m<\/mml:mi>e<\/mml:mi>n<\/mml:mi>t<\/mml:mi><\/mml:math>, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality<\/mml:mtext><\/mml:mrow><\/mml:math>, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.<\/jats:p>","DOI":"10.22331\/q-2023-12-04-1194","type":"journal-article","created":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T13:39:01Z","timestamp":1701697141000},"page":"1194","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":15,"title":["Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory"],"prefix":"10.22331","volume":"7","author":[{"given":"David","family":"Schmid","sequence":"first","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5"},{"name":"Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"},{"name":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas C.","family":"Fraser","sequence":"additional","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5"},{"name":"Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ravi","family":"Kunjwal","sequence":"additional","affiliation":[{"name":"Centre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, CP 165, Universit\u00e9 libre de Bruxelles, 1050 Brussels, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ana Belen","family":"Sainz","sequence":"additional","affiliation":[{"name":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elie","family":"Wolfe","sequence":"additional","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert W.","family":"Spekkens","sequence":"additional","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario Canada N2L 2Y5"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,12,4]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"E. 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