{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:35:33Z","timestamp":1769214933122,"version":"3.49.0"},"reference-count":80,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T00:00:00Z","timestamp":1733875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12174221"],"award-info":[{"award-number":["12174221"]}]},{"name":"National Natural Science Foundation of China","award":["12234013"],"award-info":[{"award-number":["12234013"]}]},{"name":"National Natural Science Foundation of China","award":["ZR0221LLZ009"],"award-info":[{"award-number":["ZR0221LLZ009"]}]},{"name":"Natural Science Foundation of Shandong Province","award":["12174221"],"award-info":[{"award-number":["12174221"]}]},{"name":"Natural Science Foundation of Shandong Province","award":["12234013"],"award-info":[{"award-number":["12234013"]}]},{"name":"Natural Science Foundation of Shandong Province","award":["ZR0221LLZ009"],"award-info":[{"award-number":["ZR0221LLZ009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The quantum Zeno effect (QZE) is widely employed in quantum engineering due to the issue of frequent measurements freezing a quantum system. In this study, the quantum Zeno factor is introduced to characterize the quantum Zeno capacity of a quantum system. The quantum Zeno factor reveals that the quantum Zeno effect is dependent on the evolution mode of quantum states, which is semi-irrelevant to conventional energy uncertainty and extends the QZE domain. The Zeno factor provides a new consideration to qualify the (anti-)Zeno capacity of a quantum system for its applications: a large quantum Zeno factor value indicates that a quantum system is of a QZE quality. The numerical results of the quantum Zeno capacity are shown using two typical examples: tailing the dynamic evolution modes using the quantum Zeno factor in a three-level system, and quantifying the message exchange between qubits in a coupled qubit system using a quantum Zeno factor.<\/jats:p>","DOI":"10.3390\/e26121080","type":"journal-article","created":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T06:44:05Z","timestamp":1733899445000},"page":"1080","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Quantum Zeno Capacity and Dynamic Evolution Mode of a Quantum System"],"prefix":"10.3390","volume":"26","author":[{"given":"Zhenbo","family":"Ni","sequence":"first","affiliation":[{"name":"School of Physics, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yonggang","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Physics, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9974-2917","authenticated-orcid":false,"given":"Yujun","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Physics, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,11]]},"reference":[{"key":"ref_1","unstructured":"von Neumann, J. 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