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Our framework is general enough to accommodate any system and measuring device (pointer) models, but for illustration we use an explicit model of an <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><\/mml:math>-particle pointer. For a pointer that perfectly reproduces the statistics of the system, we provide tight analytic expressions for the energy cost of performing the measurement. This cost may be broken down into two parts. First, the cost of preparing the pointer in a suitable state, and second, the cost of a global interaction between the system and pointer in order to correlate them. Our results show that, even under the assumption that the interaction can be controlled perfectly, achieving perfect correlation is infinitely expensive. We provide protocols for achieving optimal correlation given finite resources for the most general system and pointer Hamiltonians, phrasing our results as fundamental bounds in terms of the dimensions of these systems.<\/jats:p>","DOI":"10.22331\/q-2020-01-13-222","type":"journal-article","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T15:26:14Z","timestamp":1578929174000},"page":"222","source":"Crossref","is-referenced-by-count":92,"title":["Ideal Projective Measurements Have Infinite Resource Costs"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9943-9424","authenticated-orcid":false,"given":"Yelena","family":"Guryanova","sequence":"first","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1950-8640","authenticated-orcid":false,"given":"Nicolai","family":"Friis","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1985-4623","authenticated-orcid":false,"given":"Marcus","family":"Huber","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2020,1,13]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Sai Vinjanampathy and Janet Anders, Quantum thermodynamics, Contemp. 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