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Given an encoding operation as a black box from a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>-dimensional system to a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><\/mml:math>-dimensional system, we propose a universal protocol for isometry inversion that constructs a decoder from multiple calls of the encoding operation. This is a probabilistic but exact protocol whose success probability is independent of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><\/mml:math>. For a qubit (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math>) encoded in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math> qubits, our protocol achieves an exponential improvement over any tomography-based or unitary-embedding method, which cannot avoid <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><\/mml:math>-dependence. We present a quantum operation that converts multiple parallel calls of any given isometry operation to random parallelized unitary operations, each of dimension <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>. Applied to our setup, it universally compresses the encoded quantum information to a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><\/mml:math>-independent space, while keeping the initial quantum information intact. This compressing operation is combined with a unitary inversion protocol to complete the isometry inversion. We also discover a fundamental difference between our isometry inversion protocol and the known unitary inversion protocols by analyzing isometry complex conjugation and isometry transposition. General protocols including indefinite causal order are searched using semidefinite programming for any improvement in the success probability over the parallel protocols. We find a sequential \"success-or-draw\" protocol of universal isometry inversion for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:math>, thus whose success probability exponentially improves over parallel protocols in the number of calls of the input isometry operation for the said case.<\/jats:p>","DOI":"10.22331\/q-2023-03-20-957","type":"journal-article","created":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T14:57:50Z","timestamp":1679324270000},"page":"957","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Universal construction of decoders from encoding black boxes"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0521-5209","authenticated-orcid":false,"given":"Satoshi","family":"Yoshida","sequence":"first","affiliation":[{"name":"Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7502-5582","authenticated-orcid":false,"given":"Akihito","family":"Soeda","sequence":"additional","affiliation":[{"name":"Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan"},{"name":"Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan"},{"name":"Department of Informatics, School of Multidisciplinary Sciences, SOKENDAI (The Graduate University for Advanced Studies), 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7861-1774","authenticated-orcid":false,"given":"Mio","family":"Murao","sequence":"additional","affiliation":[{"name":"Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan"},{"name":"Trans-scale Quantum Science Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2023,3,20]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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