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We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermore, we study the relationship between A-unital channels and other classes of channels pertinent to the resource theory of entanglement. We then prove similar results for ACVENN: a previously defined, relevant class of states and also relate the maximum and minimum conditional entropy of a state with its von Neumann entropy.\nThe definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, our work is valuable for the detection of resourceful channels in the context of conditional entropy.<\/jats:p>","DOI":"10.22331\/q-2022-02-02-641","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T16:27:12Z","timestamp":1643819232000},"page":"641","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["A-unital Operations and Quantum Conditional Entropy"],"prefix":"10.22331","volume":"6","author":[{"given":"Mahathi","family":"Vempati","sequence":"first","affiliation":[{"name":"Centre for Quantum Science and Technology, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana-500032, India."},{"name":"Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana-500032, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saumya","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nirman","family":"Ganguly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad Campus, Telangana-500078, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indranil","family":"Chakrabarty","sequence":"additional","affiliation":[{"name":"Centre for Quantum Science and Technology, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana-500032, India."},{"name":"Center for Security, Theory and Algorithmic Research, International Institute of Information Technology-Hyderabad, Gachibowli, Telangana-500032, India."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Ryszard Horodecki, Pawe\u0142 Horodecki, Micha\u0142 Horodecki, and Karol Horodecki. 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