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The standard approach to this problem is to study approximate or probabilistic transformations. Here, we investigate the intermediate regime, providing limits on both, the fidelity and the probability of state transformations. We derive limitations on the transformations, which are valid in all quantum resource theories, by providing bounds on the maximal transformation fidelity for a given transformation probability. As an application, we show that these bounds imply an upper bound on the asymptotic rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels, which goes beyond the previously known bounds of channel manipulations. Furthermore, we completely solve the question of stochastic-approximate state conversion via local operations and classical communication in the following two cases: (i) Both initial and target states are pure bipartite entangled states of arbitrary dimensions. (ii) The target state is a two-qubit entangled state and the initial state is a pure bipartite state.<\/jats:p>","DOI":"10.22331\/q-2025-12-05-1929","type":"journal-article","created":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T09:35:16Z","timestamp":1764927316000},"page":"1929","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic approximate state conversion for entanglement and general quantum resource theories"],"prefix":"10.22331","volume":"9","author":[{"given":"Tulja Varun","family":"Kondra","sequence":"first","affiliation":[{"name":"Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland"},{"name":"Institute for Theoretical Physics III, Heinrich Heine University D\u00fcsseldorf, Universit\u00e4tsstra\u00dfe 1, D-40225 D\u00fcsseldorf, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chandan","family":"Datta","sequence":"additional","affiliation":[{"name":"Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland"},{"name":"Department of Physics, Indian Institute of Technology Jodhpur, Jodhpur 342030, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Streltsov","sequence":"additional","affiliation":[{"name":"Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawi\u0144skiego 5B, 02-106 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2025,12,5]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Eric Chitambar and Gilad Gour. ``Quantum resource theories''. 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