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Quantum games model interactions between strategic players who have access to quantum resources, and several recent works have studied learning in the competitive regime of quantum zero-sum games. Going beyond this setting, we introduce quantum common-interest games (CIGs) where players have density matrices as strategies and their interests are perfectly aligned. We bridge the gap between optimization and game theory by establishing the equivalence between KKT (first-order stationary) points of an instance of the Best Separable State (BSS) problem and the Nash equilibria of its corresponding quantum CIG. This allows learning dynamics for the quantum CIG to be seen as decentralized algorithms for the BSS problem. Taking the perspective of learning in games, we then introduce non-commutative extensions of the continuous-time replicator dynamics and the discrete-time best response dynamics\/linear multiplicative weights update for learning in quantum CIGs. We prove analogues of classical convergence results of the dynamics and explore differences which arise in the quantum setting. Finally, we corroborate our theoretical findings through extensive experiments.<\/jats:p>","DOI":"10.22331\/q-2025-04-03-1689","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T02:57:53Z","timestamp":1743735473000},"page":"1689","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Learning in Quantum Common-Interest Games and the Separability Problem"],"prefix":"10.22331","volume":"9","author":[{"given":"Wayne","family":"Lin","sequence":"first","affiliation":[{"name":"Singapore University of Technology and Design, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georgios","family":"Piliouras","sequence":"additional","affiliation":[{"name":"Singapore University of Technology and Design, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryann","family":"Sim","sequence":"additional","affiliation":[{"name":"Singapore University of Technology and Design, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonios","family":"Varvitsiotis","sequence":"additional","affiliation":[{"name":"Singapore University of Technology and Design, Singapore"},{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore"},{"name":"Archimedes\/Athena RC, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Matej Morav\u010d\u00edk, Martin Schmid, Neil Burch, Viliam Lis\u1ef3, Dustin Morrill, Nolan Bard, Trevor Davis, Kevin Waugh, Michael Johanson, and Michael Bowling. ``Deepstack: Expert-level artificial intelligence in heads-up no-limit poker''. 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