{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:47:49Z","timestamp":1760150869741,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,22]],"date-time":"2022-01-22T00:00:00Z","timestamp":1642809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11775084"],"award-info":[{"award-number":["11775084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For a fixed pair of input and output states in the space HA of a system A, a quantum channel, i.e., a linear, completely positive and trace-preserving map, between them is not unique, in general. Here, this point is discussed specifically for a decoherence channel, which maps from a pure input state to a completely decoherent state like the thermal state. In particular, decoherence channels of two different types are analyzed: one is unital and the other is not, and both of them can be constructed through reduction of B in the total extended space HA\u2297HB, where HB is the space of an ancillary system B that is a replica of A. The nonuniqueness is seen to have its origin in the unitary symmetry in the extended space. It is shown in an example of a two-qubit system how such symmetry is broken in the objective subspace HA due to entanglement between A and B. A comment is made on possible relevance of the present work to nanothermodynamics in view of quantum Darwinism.<\/jats:p>","DOI":"10.3390\/sym14020214","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:36:27Z","timestamp":1642970187000},"page":"214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Nonuniqueness of Quantum Channel for Fixed Input-Output States: Case of Decoherence Channel"],"prefix":"10.3390","volume":"14","author":[{"given":"Congjie","family":"Ou","sequence":"first","affiliation":[{"name":"Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumiyoshi","family":"Abe","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China"},{"name":"Institute of Physics, Kazan Federal University, Kazan 420008, Russia"},{"name":"Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent, Tashkent 100095, Uzbekistan"},{"name":"ESIEA, 9 Rue Vesale, 75005 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Schumacher, B., and Westmoreland, M. 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