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In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cram\u00e9r-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.<\/jats:p>","DOI":"10.22331\/q-2020-07-02-288","type":"journal-article","created":{"date-parts":[[2020,7,2]],"date-time":"2020-07-02T17:47:57Z","timestamp":1593712077000},"page":"288","source":"Crossref","is-referenced-by-count":40,"title":["Optimal probes and error-correction schemes in multi-parameter quantum metrology"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9912-9186","authenticated-orcid":false,"given":"Wojciech","family":"G\u00f3recki","sequence":"first","affiliation":[{"name":"Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4618-8590","authenticated-orcid":false,"given":"Sisi","family":"Zhou","sequence":"additional","affiliation":[{"name":"Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA"},{"name":"Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA"},{"name":"Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0000-9342","authenticated-orcid":false,"given":"Liang","family":"Jiang","sequence":"additional","affiliation":[{"name":"Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA"},{"name":"Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA"},{"name":"Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5550-4431","authenticated-orcid":false,"given":"Rafa\u0142","family":"Demkowicz-Dobrza\u0144ski","sequence":"additional","affiliation":[{"name":"Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2020,7,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"V. 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McKenzie, D. A. Shaddock, D. E. McClelland, B. C. Buchler, and P. K. Lam, Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection, Phys. Rev. Lett. 88, 231102 (2002).","DOI":"10.1103\/PhysRevLett.88.231102"},{"key":"14","doi-asserted-by":"publisher","unstructured":"J. Bollinger, W. M. Itano, D. Wineland, and D. Heinzen, Optimal frequency measurements with maximally correlated states, Phys. Rev. A 54, R4649 (1996).","DOI":"10.1103\/PhysRevA.54.R4649"},{"key":"15","doi-asserted-by":"publisher","unstructured":"D. Leibfried, M. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. Itano, J. Jost, C. Langer, and D. Wineland, Toward heisenberg-limited spectroscopy with multiparticle entangled states, Science 304, 1476 (2004).","DOI":"10.1126\/science.1097576"},{"key":"16","doi-asserted-by":"publisher","unstructured":"V. Giovannetti, S. Lloyd, and L. 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