{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T01:10:38Z","timestamp":1776215438358,"version":"3.50.1"},"reference-count":23,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2021,1,17]],"date-time":"2021-01-17T00:00:00Z","timestamp":1610841600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Division of Materials Research - National Science Foundation","award":["1939864"],"award-info":[{"award-number":["1939864"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the ``mixed'' phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo>\u2014<\/mml:mo><\/mml:math>i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo>\u2014<\/mml:mo><\/mml:math>purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.<\/jats:p>","DOI":"10.22331\/q-2021-01-17-382","type":"journal-article","created":{"date-parts":[[2021,1,17]],"date-time":"2021-01-17T19:18:01Z","timestamp":1610911081000},"page":"382","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":84,"title":["How Dynamical Quantum Memories Forget"],"prefix":"10.22331","volume":"5","author":[{"given":"Lukasz","family":"Fidkowski","sequence":"first","affiliation":[{"name":"Department of Physics, University of Washington, Seattle, WA 98195-1560, USA"}]},{"given":"Jeongwan","family":"Haah","sequence":"additional","affiliation":[{"name":"Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA"}]},{"given":"Matthew B.","family":"Hastings","sequence":"additional","affiliation":[{"name":"Station Q, Microsoft Research, Santa Barbara, CA 93106-6105, USA"},{"name":"Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA"}]}],"member":"9598","published-online":{"date-parts":[[2021,1,17]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Y. 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