{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T18:19:24Z","timestamp":1769019564783,"version":"3.49.0"},"reference-count":99,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T00:00:00Z","timestamp":1565568000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancillary systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel's Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancillary systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case.Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>\u2113<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:math>-norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.<\/jats:p>","DOI":"10.22331\/q-2019-08-12-171","type":"journal-article","created":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T09:02:04Z","timestamp":1565600524000},"page":"171","source":"Crossref","is-referenced-by-count":24,"title":["Guaranteed recovery of quantum processes from few measurements"],"prefix":"10.22331","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8009-0549","authenticated-orcid":false,"given":"Martin","family":"Kliesch","sequence":"first","affiliation":[{"name":"Institute for Theoretical Physics, Heinrich Heine University D\u00fcsseldorf, Germany"},{"name":"Institute of Theoretical Physics and Astrophysics, University of Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard","family":"Kueng","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, University of Cologne, Germany"},{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, Germany"},{"name":"Institute for Quantum Information and Matter, California Institute of Technology, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jens","family":"Eisert","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, Germany"},{"name":"Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, Germany"},{"name":"Helmholtz-Zentrum Berlin f\u00fcr Materialien und Energie, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Gross","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, University of Cologne, Germany"},{"name":"Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2019,8,12]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"I. 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