{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:04:36Z","timestamp":1760058276228,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T00:00:00Z","timestamp":1743033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shandong Province","award":["ZR2023LLZ004","ZR2022QA018","ZR2021LLZ011","12204355","52272210","2023GX017","2021GX010"],"award-info":[{"award-number":["ZR2023LLZ004","ZR2022QA018","ZR2021LLZ011","12204355","52272210","2023GX017","2021GX010"]}]},{"name":"Natural Science Foundation of China","award":["ZR2023LLZ004","ZR2022QA018","ZR2021LLZ011","12204355","52272210","2023GX017","2021GX010"],"award-info":[{"award-number":["ZR2023LLZ004","ZR2022QA018","ZR2021LLZ011","12204355","52272210","2023GX017","2021GX010"]}]},{"name":"Weifang Science and Technology Development Plan Foundation","award":["ZR2023LLZ004","ZR2022QA018","ZR2021LLZ011","12204355","52272210","2023GX017","2021GX010"],"award-info":[{"award-number":["ZR2023LLZ004","ZR2022QA018","ZR2021LLZ011","12204355","52272210","2023GX017","2021GX010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The study of system evolution in generalized amplitude damping is of great significance in quantum information science and quantum computing. As an important quantum noise channel, the generalized amplitude damping channel can describe the general phenomenon of the energy dissipation effect in quantum systems at finite temperature. In this paper, we study the use of weak measurement and reversal to protect the entanglement of X-type systems in generalized amplitude damping channels, and give an experimental scheme. The results show that the closer to zero the temperature environment, the better the protection effect of weak measurement and reversal, but the lower the success rate. Therefore, when choosing an experimental environment, it is important to consider not only the temperature factor but also the probability of success. Because all quantum systems work at finite temperatures, it is hoped that the study of generalized amplitude damping channels can help design more robust quantum algorithms and protocols to improve the efficiency and stability of quantum information processing.<\/jats:p>","DOI":"10.3390\/e27040350","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T04:36:48Z","timestamp":1743136608000},"page":"350","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Protecting the Entanglement of X-Type Systems via Weak Measurement and Reversal in the Generalized Amplitude Damping Channel"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5759-7256","authenticated-orcid":false,"given":"Meijiao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]},{"given":"Haojie","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]},{"given":"Lianzhen","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]},{"given":"Yang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]},{"given":"Xia","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]},{"given":"Bing","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]},{"given":"Jiaqiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information, Weifang University, Weifang 261061, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1103\/RevModPhys.81.865","article-title":"Quantum entanglement","volume":"81","author":"Horodedecki","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"012101","DOI":"10.1103\/PhysRevA.65.012101","article-title":"Dynamics of quantum entanglement","volume":"86","author":"Zyczkowski","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1038\/35089017","article-title":"Sub-planck structure in phase space and its relevance for quantum decoherence","volume":"412","author":"Zurek","year":"2001","journal-title":"Nature"},{"key":"ref_4","first-page":"012331","article-title":"Unified framework for quantumness\u2013coherence, discord, and entanglement","volume":"97","author":"Xiao","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1103\/PhysRevLett.60.1351","article-title":"How the result of a component of the spin of a spin-1\/2 particle can turn out to be 100","volume":"60","author":"Aharonov","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0375-9601(87)90619-0","article-title":"Surprising quantum effects","volume":"124","author":"Aharonov","year":"1987","journal-title":"Phys. Lett. A"},{"key":"ref_7","first-page":"19","article-title":"Improving the capacity of quantum dense coding by weak measurement and reversal measurement","volume":"19","author":"Tian","year":"2018","journal-title":"Quantum Inf. Comput."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3067","DOI":"10.1007\/s11128-013-0585-x","article-title":"Recovering quantum correlations from amplitude damping decoherence by weak measurement reversal","volume":"12","author":"Li","year":"2013","journal-title":"Quantum Inf. Process"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"200201","DOI":"10.1103\/PhysRevLett.131.200201","article-title":"Nishimori\u2019s cat: Stable long-range entanglement from finite-depth unitaries and weak measurements","volume":"131","author":"Zhu","year":"2023","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"040324","DOI":"10.1103\/PRXQuantum.4.040324","article-title":"Time-dependent hamiltonian reconstruction using continuous weak measurements","volume":"4","author":"Siva","year":"2023","journal-title":"PRX Quantum"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1007\/s10773-012-1367-4","article-title":"Amplitude damping decoherence suppression of two-qubit entangled states by weak measurements","volume":"52","author":"Tan","year":"2013","journal-title":"Int. J. Theor. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"11978","DOI":"10.1364\/OE.17.011978","article-title":"Reversing the weak quantum measurement for a photonic qubit","volume":"17","author":"Kim","year":"2009","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"040103","DOI":"10.1103\/PhysRevA.81.040103","article-title":"Decoherence suppression by quantum measurement reversal","volume":"81","author":"Korotkov","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"012325","DOI":"10.1103\/PhysRevA.86.012325","article-title":"Manipulating entanglement of two qubits in a commom environment by means of weak measurement and quantum measurement reversals","volume":"86","author":"Man","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"052322","DOI":"10.1103\/PhysRevA.86.052322","article-title":"Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements","volume":"86","author":"Man","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"052323","DOI":"10.1103\/PhysRevA.82.052323","article-title":"Reversing entanglement change by weak measurement","volume":"82","author":"Sun","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1038\/nphys2178","article-title":"Protecting entanglement from decoherence using weak measurement and quantum measurement reversal","volume":"8","author":"Kim","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"065102","DOI":"10.1088\/0031-8949\/89\/6\/065102","article-title":"Protecting qubit-qutrit entanglement from amplitude damping decoherence via weak measurement and reversal","volume":"89","author":"Xiao","year":"2014","journal-title":"Phys. Scr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1140\/epjd\/e2013-40036-3","article-title":"Protecting qutrit-qutrit entanglement by weak measurement and reversal","volume":"67","author":"Xiao","year":"2013","journal-title":"Eur. Phys. J. D"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"110307","DOI":"10.1088\/1674-1056\/aba614","article-title":"Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal","volume":"29","author":"Wang","year":"2020","journal-title":"Chin. Phys. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4096","DOI":"10.1364\/OE.449724","article-title":"Optimal weak measurement in the photonic spin Hall effect for arbitrary linear polarization incidence","volume":"30","author":"Lin","year":"2022","journal-title":"Opt. Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"130283","DOI":"10.1016\/j.optcom.2024.130283","article-title":"Optimized weak measurement model for in-plane and out-of-plane splitting shifts of Photonic Spin Hall effect","volume":"557","author":"Qin","year":"2024","journal-title":"Opt. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"100403","DOI":"10.1103\/PhysRevLett.126.100403","article-title":"Weak measurement of a superconducting qubit reconciles incompatible operators","volume":"126","author":"Monroe","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"033838","DOI":"10.1103\/PhysRevA.80.033838","article-title":"Reversing the weak measurement of an arbitrary field with finite photon number","volume":"80","author":"Sun","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s11128-023-04203-x","article-title":"On super quantum discord for high-dimensional bipartite state","volume":"22","author":"Zhou","year":"2023","journal-title":"Quantum Inf. Process"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"R773","DOI":"10.1103\/PhysRevA.60.R773","article-title":"Ultrabright source of polarization-entangled photons","volume":"60","author":"Kwiat","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s11128-018-2114-4","article-title":"Enhance quantum teleportation under correlated amplitude damping deocherence by weak measurement and quantum measurement reversal","volume":"18","author":"Li","year":"2019","journal-title":"Quantum Inf. Process"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s11128-021-02998-1","article-title":"Enhancing the teleportation of quantum Fisher information by weak measurement and environment-assisted measurement","volume":"20","author":"Li","year":"2021","journal-title":"Quantum Inf. Process"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"050306","DOI":"10.1088\/1674-1056\/acbd2a","article-title":"Quantum state protection from finite-temperature thermal noise with application to controlled quantum teleportation","volume":"32","author":"Wang","year":"2023","journal-title":"Chin. Phys. B"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"110302","DOI":"10.1088\/1674-1056\/abf34f","article-title":"Dense coding capacity in correlated noisy channels with weak measurement","volume":"30","author":"Li","year":"2021","journal-title":"Chin. Phys. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"042342","DOI":"10.1103\/PhysRevA.95.042342","article-title":"Protecting entanglement from finite-temperature thermal noise via weak measurement and quantum measurement reversal","volume":"95","author":"Zou","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"022318","DOI":"10.1103\/PhysRevA.89.022318","article-title":"Protecting quantum states from decoherence of finite temperature using weak measurement","volume":"89","author":"Wang","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"042204","DOI":"10.1103\/PhysRevA.110.042204","article-title":"Evidence of genuine quantum effects in nonequilibrium entropy production via quantum photonics","volume":"110","author":"Xue","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1103\/PhysRevLett.80.2245","article-title":"Entanglement of formation of an arbitrary state of two qubits","volume":"80","author":"Wootters","year":"1998","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/4\/350\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:03:43Z","timestamp":1760029423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/4\/350"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,27]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["e27040350"],"URL":"https:\/\/doi.org\/10.3390\/e27040350","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,3,27]]}}}