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Wilde raised the question of whether the monotonicity of optimized quantum<jats:italic>f<\/jats:italic>-divergence can be generalized to maps that are not quantum channels. In this paper, we answer this question by generalizing the monotonicity of optimized quantum<jats:italic>f<\/jats:italic>-divergences to positive trace preserving maps satisfying a Schwarz inequality. Any 2-positive maps satisfy such a Schwarz inequality. The main tool in this paper is the Petz recovery map.<\/jats:p>","DOI":"10.1007\/s11128-024-04376-z","type":"journal-article","created":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T14:01:53Z","timestamp":1714831313000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Monotonicity of optimized quantum f-divergence"],"prefix":"10.1007","volume":"23","author":[{"given":"Haojian","family":"Li","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,4]]},"reference":[{"key":"4376_CR1","doi-asserted-by":"crossref","unstructured":"Umegaki, H.: Conditional expectation in an operator algebra, iv (entropy and information). In: Kodai Mathematical Seminar Reports, vol 14, pp 59\u201385. 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