{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T07:40:08Z","timestamp":1747208408572,"version":"3.40.5"},"reference-count":45,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T00:00:00Z","timestamp":1714953600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Moonshot R&D","award":["JPMJMS2061"],"award-info":[{"award-number":["JPMJMS2061"]}]},{"DOI":"10.13039\/100018237","name":"Asian Office of Aerospace Research and Development","doi-asserted-by":"crossref","award":["FA2386-20-1-4069"],"award-info":[{"award-number":["FA2386-20-1-4069"]}],"id":[{"id":"10.13039\/100018237","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N62909-23-1-2074"],"award-info":[{"award-number":["N62909-23-1-2074"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["PHY-2011382"],"award-info":[{"award-number":["PHY-2011382"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["PZ00P2-208885"],"award-info":[{"award-number":["PZ00P2-208885"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000925","name":"John Templeton Foundation","doi-asserted-by":"crossref","award":["62312"],"award-info":[{"award-number":["62312"]}],"id":[{"id":"10.13039\/100000925","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["PHY-2011382"],"award-info":[{"award-number":["PHY-2011382"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"In physics, it is crucial to identify operational measurement procedures to give physical meaning to abstract quantities. There has been significant effort to define time operationally using quantum systems, but the same has not been achieved for space. Developing an operational procedure to obtain information about the location of a quantum system is particularly important for a theory combining general relativity and quantum theory, which cannot rest on the classical notion of spacetime. Here, we take a first step towards this goal, and introduce a model to describe an extended material quantum system working as a position measurement device. Such a \"quantum ruler\" is composed of N<\/mml:mi><\/mml:math> harmonically interacting dipoles and serves as a (quantum) reference system for the position of another quantum system. We show that we can define a quantum measurement procedure corresponding to the \"superposition of positions\", and that by performing this measurement we can distinguish when the quantum system is in a coherent or incoherent superposition in the position basis. The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system, and the measurement is expressed in terms of an interaction between the measurement device and the measured system.<\/jats:p>","DOI":"10.22331\/q-2024-05-06-1335","type":"journal-article","created":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T12:18:53Z","timestamp":1714997933000},"page":"1335","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Relational superposition measurements with a material quantum ruler"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1012-1124","authenticated-orcid":false,"given":"Hui","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA"},{"name":"Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2475-2296","authenticated-orcid":false,"given":"Flaminia","family":"Giacomini","sequence":"additional","affiliation":[{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada"},{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, Wolfgang-Pauli-Str. 27, Z\u00fcrich, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3682-7432","authenticated-orcid":false,"given":"Franco","family":"Nori","sequence":"additional","affiliation":[{"name":"Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama 351-0198, Japan"},{"name":"Quantum Computing Center, RIKEN, Wako-shi, Saitama 351-0198, Japan"},{"name":"Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0051-0492","authenticated-orcid":false,"given":"Miles P.","family":"Blencowe","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA"}]}],"member":"9598","published-online":{"date-parts":[[2024,5,6]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Asher Peres, Petra F. 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