{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:33:04Z","timestamp":1760236384716,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T00:00:00Z","timestamp":1637107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent\u2019s perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.<\/jats:p>","DOI":"10.3390\/e23111527","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T21:32:07Z","timestamp":1637184727000},"page":"1527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Limits to Perception by Quantum Monitoring with Finite Efficiency"],"prefix":"10.3390","volume":"23","author":[{"given":"Luis Pedro","family":"Garc\u00eda-Pintos","sequence":"first","affiliation":[{"name":"Department of Physics, University of Massachusetts, Boston, MA 02125, USA"},{"name":"Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST\/University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2219-2851","authenticated-orcid":false,"given":"Adolfo","family":"del Campo","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Massachusetts, Boston, MA 02125, USA"},{"name":"Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg"},{"name":"Donostia International Physics Center, E-20018 San Sebasti\u00e1n, Spain"},{"name":"IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1080\/00107510601101934","article-title":"A straightforward introduction to continuous quantum measurement","volume":"47","author":"Jacobs","year":"2006","journal-title":"Contemp. 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