{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T17:14:14Z","timestamp":1781630054773,"version":"3.54.5"},"reference-count":69,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T00:00:00Z","timestamp":1500940800000},"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>The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.<\/jats:p>","DOI":"10.22331\/q-2017-07-25-20","type":"journal-article","created":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T08:02:48Z","timestamp":1500969768000},"page":"20","source":"Crossref","is-referenced-by-count":13,"title":["Uncertainty relations: An operational approach to the error-disturbance tradeoff"],"prefix":"10.22331","volume":"1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2302-8025","authenticated-orcid":false,"given":"Joseph M.","family":"Renes","sequence":"first","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3235-022X","authenticated-orcid":false,"given":"Volkher B.","family":"Scholz","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, Switzerland"},{"name":"Department of Physics, Ghent University, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0564-5436","authenticated-orcid":false,"given":"Stefan","family":"Huber","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, Switzerland"},{"name":"Department of Mathematics, Technische Universit\u00e4t M\u00fcnchen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2017,7,25]]},"reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"Heisenberg ``\u00dcber Den Anschaulichen Inhalt'' Zeitschrift f\u00fcr Physik 43, 172-198 (1927).","DOI":"10.1007\/BF01397280"},{"key":"2","unstructured":"Wheelerand Zurek ``Quantum Theory'' Princeton University Press (1984)."},{"key":"3","doi-asserted-by":"publisher","unstructured":"Kennard ``Zur Quantenmechanik'' Zeitschrift f\u00fcr Physik 44, 326-352 (1927).","DOI":"10.1007\/BF01391200"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Robertson ``The Uncertainty Principle'' Physical Review 34, 163 (1929).","DOI":"10.1103\/PhysRev.34.163"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Maassenand Uffink ``Generalized Entropic Uncertainty Relations'' Physical Review Letters 60, 1103 (1988).","DOI":"10.1103\/PhysRevLett.60.1103"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Berta, Christandl, Colbeck, Renes, and Renner, ``The Uncertainty Principle in the Presence of Quantum Memory'' Nature Physics 6, 659-662 (2010).","DOI":"10.1038\/nphys1734"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Coles, Berta, Tomamichel, and Wehner, ``Entropic Uncertainty Relations and Their Applications'' Reviews of Modern Physics 89, 015002 (2017).","DOI":"10.1103\/RevModPhys.89.015002"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Arthursand Kelly ``On the Simultaneous Measurement'' Bell System Technical Journal 44, 725-729 (1965).","DOI":"10.1002\/j.1538-7305.1965.tb01684.x"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Sheand Heffner ``Simultaneous Measurement'' Physical Review 152, 1103-1110 (1966).","DOI":"10.1103\/PhysRev.152.1103"},{"key":"10","unstructured":"Davies ``Quantum Theory of Open Systems'' Academic Press (1976)."},{"key":"11","doi-asserted-by":"publisher","unstructured":"Aliand Prugove\u010dki ``Systems of Imprimitivity and Representations of Quantum Mechanics on Fuzzy Phase Spaces'' Journal of Mathematical Physics 18, 219-228 (1977).","DOI":"10.1063\/1.523259"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Prugove\u010dki ``On Fuzzy Spin Spaces'' Journal of Physics A: Mathematical and General 10, 543 (1977).","DOI":"10.1088\/0305-4470\/10\/4\/016"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Busch ``Indeterminacy Relations and Simultaneous Measurements in Quantum Theory'' International Journal of Theoretical Physics 24, 63-92 (1985).","DOI":"10.1007\/BF00670074"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Busch ``Unsharp Reality and Joint Measurements for Spin Observables'' Physical Review D 33, 2253-2261 (1986).","DOI":"10.1103\/PhysRevD.33.2253"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Arthursand Goodman ``Quantum Correlations'' Physical Review Letters 60, 2447-2449 (1988).","DOI":"10.1103\/PhysRevLett.60.2447"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Martensand W. 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