{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T22:59:48Z","timestamp":1773788388490,"version":"3.50.1"},"reference-count":98,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T00:00:00Z","timestamp":1622678400000},"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 address the problem of entanglement protection against surrounding noise by a procedure suitably exploiting spatial indistinguishability of identical subsystems. To this purpose, we take two initially separated and entangled identical qubits interacting with two independent noisy environments. Three typical models of environments are considered: amplitude damping channel, phase damping channel and depolarizing channel. After the interaction, we deform the wave functions of the two qubits to make them spatially overlap before performing spatially localized operations and classical communication (sLOCC) and eventually computing the entanglement of the resulting state. This way, we show that spatial indistinguishability of identical qubits can be utilized within the sLOCC operational framework to partially recover the quantum correlations spoiled by the environment. A general behavior emerges: the higher the spatial indistinguishability achieved via deformation, the larger the amount of recovered entanglement.<\/jats:p>","DOI":"10.3390\/e23060708","type":"journal-article","created":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T10:59:51Z","timestamp":1622717991000},"page":"708","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Entanglement Robustness via Spatial Deformation of Identical Particle Wave Functions"],"prefix":"10.3390","volume":"23","author":[{"given":"Matteo","family":"Piccolini","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy"},{"name":"INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farzam","family":"Nosrati","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy"},{"name":"INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Compagno","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Chimica\u2014Emilio Segr\u00e8, Universit\u00e0 di Palermo, via Archirafi 36, 90123 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8599-0418","authenticated-orcid":false,"given":"Patrizia","family":"Livreri","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"Morandotti","sequence":"additional","affiliation":[{"name":"INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3281-0935","authenticated-orcid":false,"given":"Rosario","family":"Lo Franco","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","article-title":"Quantum Computing in the NISQ era and beyond","volume":"2","author":"Preskill","year":"2018","journal-title":"Quantum"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"114001","DOI":"10.1088\/0034-4885\/78\/11\/114001","article-title":"A review of progress in the physics of open quantum systems: Theory and experiment","volume":"78","author":"Rotter","year":"2015","journal-title":"Rep. Prog. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1098\/rspa.1998.0167","article-title":"Reliable quantum computers","volume":"454","author":"Preskill","year":"1998","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1038\/nature03350","article-title":"Quantum computing with realistically noisy devices","volume":"434","author":"Knill","year":"2005","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"R2493","DOI":"10.1103\/PhysRevA.52.R2493","article-title":"Scheme for reducing decoherence in quantum computer memory","volume":"52","author":"Shor","year":"1995","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1103\/PhysRevLett.77.793","article-title":"Error correcting codes in quantum theory","volume":"77","author":"Steane","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"042302","DOI":"10.1103\/PhysRevA.79.042302","article-title":"Sudden death and sudden birth of entanglement in common structured reservoirs","volume":"79","author":"Mazzola","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"060302","DOI":"10.1103\/PhysRevA.78.060302","article-title":"Entanglement trapping in structured environments","volume":"78","author":"Bellomo","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1345053","DOI":"10.1142\/S0217979213450537","article-title":"Dynamics of quantum correlations in two-qubit systems within non-Markovian environments","volume":"27","author":"Bellomo","year":"2013","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"042001","DOI":"10.1088\/0034-4885\/78\/4\/042001","article-title":"Open-system dynamics of entanglement: A key issues review","volume":"78","author":"Aolita","year":"2015","journal-title":"Rep. Prog. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"100502","DOI":"10.1103\/PhysRevLett.104.100502","article-title":"Experimental demonstration of photonic entanglement collapse and revival","volume":"104","author":"Xu","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep05720","article-title":"Non-Markovianity and reservoir memory of quantum channels: A quantum information theory perspective","volume":"4","author":"Bylicka","year":"2014","journal-title":"Sci. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep13843","article-title":"Cavity-based architecture to preserve quantum coherence and entanglement","volume":"5","author":"Man","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"062119","DOI":"10.1103\/PhysRevA.81.062119","article-title":"Non-Markovian environments and entanglement preservation","volume":"81","author":"Tan","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"052330","DOI":"10.1103\/PhysRevA.81.052330","article-title":"Mechanism of entanglement preservation","volume":"81","author":"Tong","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"021002","DOI":"10.1103\/RevModPhys.88.021002","article-title":"Colloquium: Non-Markovian dynamics in open quantum systems","volume":"88","author":"Breuer","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"012315","DOI":"10.1103\/PhysRevA.92.012315","article-title":"Harnessing non-Markovian quantum memory by environmental coupling","volume":"92","author":"Man","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1103\/PhysRevLett.76.722","article-title":"Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels","volume":"76","author":"Bennett","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1038\/35059017","article-title":"Experimental entanglement distillation and \u2018hidden\u2019non-locality","volume":"409","author":"Kwiat","year":"2001","journal-title":"Nature"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1038\/nphys1112","article-title":"Experimental entanglement distillation of mesoscopic quantum states","volume":"4","author":"Dong","year":"2008","journal-title":"Nat. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3306","DOI":"10.1103\/PhysRevLett.79.3306","article-title":"Noiseless quantum codes","volume":"79","author":"Zanardi","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2594","DOI":"10.1103\/PhysRevLett.81.2594","article-title":"Decoherence-free subspaces for quantum computation","volume":"81","author":"Lidar","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2733","DOI":"10.1103\/PhysRevA.58.2733","article-title":"Dynamical suppression of decoherence in two-state quantum systems","volume":"58","author":"Viola","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"060502","DOI":"10.1103\/PhysRevLett.94.060502","article-title":"Random decoupling schemes for quantum dynamical control and error suppression","volume":"94","author":"Viola","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.aop.2014.07.021","article-title":"Recovering entanglement by local operations","volume":"350","author":"Franco","year":"2014","journal-title":"Ann. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"054304","DOI":"10.1103\/PhysRevB.90.054304","article-title":"Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling","volume":"90","author":"Falci","year":"2014","journal-title":"Phys. Rev. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/srep08575","article-title":"Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics","volume":"5","author":"Orieux","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"032314","DOI":"10.1103\/PhysRevA.69.032314","article-title":"Unification of dynamical decoupling and the quantum Zeno effect","volume":"69","author":"Facchi","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"032318","DOI":"10.1103\/PhysRevA.85.032318","article-title":"Revival of quantum correlations without system-environment back-action","volume":"85","author":"Franco","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms3851","article-title":"Experimental recovery of quantum correlations in absence of system-environment back-action","volume":"4","author":"Xu","year":"2013","journal-title":"Nat. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"040502","DOI":"10.1103\/PhysRevLett.103.040502","article-title":"Experimental inhibition of decoherence on flying qubits via \u201cbang-bang\u201d control","volume":"103","author":"Damodarakurup","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"012314","DOI":"10.1103\/PhysRevA.96.012314","article-title":"Cut-and-paste restoration of entanglement transmission","volume":"96","author":"Cuevas","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1038\/nature08812","article-title":"Quantum computers","volume":"464","author":"Ladd","year":"2010","journal-title":"Nature"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"017003","DOI":"10.1103\/PRXQuantum.2.017003","article-title":"Quantum Simulators: Architectures and Opportunities","volume":"2","author":"Altman","year":"2021","journal-title":"PRX Quantum"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"192001","DOI":"10.1088\/0953-4075\/44\/19\/192001","article-title":"Essential entanglement for atomic and molecular physics","volume":"44","author":"Tichy","year":"2011","journal-title":"J. Phys. B At. Mol. Opt. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"012109","DOI":"10.1103\/PhysRevA.70.012109","article-title":"General criterion for the entanglement of two indistinguishable particles","volume":"70","author":"Ghirardi","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"461001","DOI":"10.1142\/S0219749914610012","article-title":"Spatial separation and entanglement of identical particles","volume":"12","author":"Cunden","year":"2014","journal-title":"Int. J. Quantum Inform."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"054302","DOI":"10.1103\/PhysRevA.64.054302","article-title":"Entanglement in a two-identical-particle system","volume":"64","author":"Li","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"042310","DOI":"10.1103\/PhysRevA.64.042310","article-title":"Quantum correlations in two-boson wave functions","volume":"64","author":"Paskauskas","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"022303","DOI":"10.1103\/PhysRevA.64.022303","article-title":"Quantum correlations in two-fermion systems","volume":"64","author":"Schliemann","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"042101","DOI":"10.1103\/PhysRevA.65.042101","article-title":"Quantum entanglement in fermionic lattices","volume":"65","author":"Zanardi","year":"2002","journal-title":"Phys. Rev. A"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1006\/aphy.2002.6268","article-title":"Quantum correlations in systems of indistinguishable particles","volume":"299","author":"Eckert","year":"2002","journal-title":"Ann. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"080503","DOI":"10.1103\/PhysRevLett.110.080503","article-title":"Entanglement and Particle Identity: A Unifying Approach","volume":"110","author":"Balachandran","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"012113","DOI":"10.1103\/PhysRevA.83.012113","article-title":"Entanglement of indistinguishable particles","volume":"83","author":"Sasaki","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1140\/epjd\/e2013-40080-y","article-title":"Entanglement in helium","volume":"67","author":"Benenti","year":"2013","journal-title":"Eur. Phys. J. D"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"050401","DOI":"10.1103\/PhysRevLett.88.050401","article-title":"Generic entanglement generation, quantum statistics, and complementarity","volume":"88","author":"Bose","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"140404","DOI":"10.1103\/PhysRevLett.110.140404","article-title":"Duality in Entanglement Enabling a Test of Quantum Indistinguishability Unaffected by Interactions","volume":"110","author":"Bose","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1002\/prop.201200079","article-title":"Entanglement of identical particles and the detection process","volume":"61","author":"Tichy","year":"2013","journal-title":"Fortschr. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"150501","DOI":"10.1103\/PhysRevLett.112.150501","article-title":"Extracting Entanglement from Identical Particles","volume":"112","author":"Killoran","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"44675","DOI":"10.1038\/srep44675","article-title":"Universality of Schmidt decomposition and particle identity","volume":"7","author":"Sciara","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"20603","DOI":"10.1038\/srep20603","article-title":"Quantum entanglement of identical particles by standard information-theoretic notions","volume":"6","author":"Compagno","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"20170317","DOI":"10.1098\/rsta.2017.0317","article-title":"Dealing with indistinguishable particles and their entanglement","volume":"376","author":"Compagno","year":"2018","journal-title":"Phil. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"240403","DOI":"10.1103\/PhysRevLett.120.240403","article-title":"Indistinguishability of elementary systems as a resource for Quantum Information Processing","volume":"120","author":"Compagno","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_54","first-page":"041012","article-title":"Entanglement between Identical Particles Is a Useful and Consistent Resource","volume":"10","author":"Morris","year":"2020","journal-title":"Phys. Rev. X"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41534-020-0271-7","article-title":"Robust entanglement preparation against noise by controlling spatial indistinguishability","volume":"6","author":"Nosrati","year":"2020","journal-title":"NPJ Quantum Inf."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"6410","DOI":"10.1364\/OL.401735","article-title":"Experimental quantum entanglement and teleportation by tuning remote spatial indistinguishability of independent photons","volume":"45","author":"Sun","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"38083","DOI":"10.1364\/OE.410361","article-title":"Entangling bosons through particle indistinguishability and spatial overlap","volume":"28","author":"Barros","year":"2020","journal-title":"Opt. Express"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"61","DOI":"10.12743\/quanta.v6i1.66","article-title":"Hanbury Brown\u2013Twiss Effect with Wave Packets","volume":"6","author":"Qureshi","year":"2017","journal-title":"Quanta"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"022314","DOI":"10.1103\/PhysRevA.101.022314","article-title":"Quantum entanglement in one-dimensional anyons","volume":"101","author":"Mani","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"062322","DOI":"10.1103\/PhysRevA.99.062322","article-title":"Activating remote entanglement in a quantum network by local counting of identical particles","volume":"99","author":"Castellini","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"012308","DOI":"10.1103\/PhysRevA.100.012308","article-title":"Indistinguishability-enabled coherence for quantum metrology","volume":"100","author":"Castellini","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_62","unstructured":"Sun, K., Liu, Z.H., Wang, Y., Hao, Z.Y., Xu, X.Y., Xu, J.S., Li, C.F., Guo, G.C., Castellini, A., and Lami, L. (2021). Experimental quantum phase discrimination enhanced by controllable indistinguishability-based coherence. arXiv."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"062429","DOI":"10.1103\/PhysRevA.102.062429","article-title":"Dynamics of spatially indistinguishable particles and quantum entanglement protection","volume":"102","author":"Nosrati","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1103\/RevModPhys.81.865","article-title":"Quantum entanglement","volume":"81","author":"Horodecki","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1142\/S0129183110015129","article-title":"A comparative study of negativity and concurrence based on spin coherent states","volume":"21","author":"Berrada","year":"2010","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1364\/JOSAB.35.000047","article-title":"Generation and robustness of bipartite non-classical correlations in two nonlinear microcavities coupled by an optical fiber","volume":"35","author":"Mohamed","year":"2018","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_67","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."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1080\/09500349414552171","article-title":"Fidelity for Mixed Quantum States","volume":"41","author":"Jozsa","year":"1994","journal-title":"J. Mod. Opt."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Breuer, H.P., and Petruccione, F. (2002). The Theory of Open Quantum Systems, Oxford University Press.","DOI":"10.1007\/3-540-44874-8_4"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Haikka, P., and Maniscalco, S. (2010). Non-Markovian dynamics of a damped driven two-state system. Phys. Rev. A, 81.","DOI":"10.1103\/PhysRevA.81.052103"},{"key":"ref_71","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Bellomo, B., Lo Franco, R., and Compagno, G. (2007). Non-Markovian Effects on the Dynamics of Entanglement. Phys. Rev. Lett., 99.","DOI":"10.1103\/PhysRevLett.99.160502"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"021314","DOI":"10.1063\/1.5088164","article-title":"Trapped-ion quantum computing: Progress and challenges","volume":"6","author":"Bruzewicz","year":"2019","journal-title":"Appl. Phys. Rev."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1038\/35002001","article-title":"Decoherence of quantum superpositions through coupling to engineered reservoirs","volume":"403","author":"Myatt","year":"2000","journal-title":"Nature"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"123012","DOI":"10.1088\/1367-2630\/15\/12\/123012","article-title":"A quantum information processor with trapped ions","volume":"15","author":"Schindler","year":"2013","journal-title":"New J. Phys."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"032314","DOI":"10.1103\/PhysRevA.71.032314","article-title":"Information-capacity description of spin-chain correlations","volume":"71","author":"Giovannetti","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"032329","DOI":"10.1103\/PhysRevA.75.032329","article-title":"Quantum-information processing with circuit quantum electrodynamics","volume":"75","author":"Blais","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1038\/s41567-020-0806-z","article-title":"Quant. Inf. Proc. and quantum optics with circuit quantum electrodynamics","volume":"16","author":"Blais","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1126\/science.1139892","article-title":"Environment-Induced Sudden Death of Entanglement","volume":"316","author":"Almeida","year":"2007","journal-title":"Science"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1007\/s11128-010-0165-2","article-title":"Disentanglement and decoherence from classical non-Markovian noise: Random telegraph noise","volume":"9","author":"Zhou","year":"2010","journal-title":"Quantum Inf. Proc."},{"key":"ref_81","first-page":"014019","article-title":"Entanglement dynamics in superconducting qubits affected by local bistable impurities","volume":"2012","author":"Falci","year":"2012","journal-title":"Phys. Scr."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1242003","DOI":"10.1142\/S0219477512420035","article-title":"Effect of Markov and non-Markov classical noise on entanglement dynamics","volume":"11","author":"Bordone","year":"2012","journal-title":"Fluc. Noise Lett."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"014004","DOI":"10.1088\/0031-8949\/2012\/T147\/014004","article-title":"Dynamics of correlations due to a phase-noisy laser","volume":"2012","author":"Bellomo","year":"2012","journal-title":"Phys. Scr."},{"key":"ref_84","first-page":"1","article-title":"Quantum dephasing induced by non-Markovian random telegraph noise","volume":"10","author":"Cai","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"205404","DOI":"10.1103\/PhysRevB.86.205404","article-title":"Decoherence of a qubit due to either a quantum fluctuator, or classical telegraph noise","volume":"86","author":"Wold","year":"2012","journal-title":"Phys. Rev. B"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1038\/s41534-018-0094-y","article-title":"Endurance of quantum coherence due to particle indistinguishability in noisy quantum networks","volume":"4","author":"Heinrich","year":"2018","journal-title":"NPJ Quantum Inf."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1103\/RevModPhys.86.361","article-title":"1\/f noise: Implications for solid-state quantum information","volume":"86","author":"Paladino","year":"2014","journal-title":"Rev. Mod. Phys."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"174306","DOI":"10.1103\/PhysRevB.76.174306","article-title":"Time evolution and decoherence of a spin-1\/2 particle coupled to a spin bath in thermal equilibrium","volume":"76","author":"Hamdouni","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"065004","DOI":"10.1088\/0031-8949\/86\/06\/065004","article-title":"Simple non-Markovian microscopic models for the depolarizing channel of a single qubit","volume":"86","author":"Romero","year":"2012","journal-title":"Phys. Scr."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"014435","DOI":"10.1103\/PhysRevB.70.014435","article-title":"Parity effects in spin decoherence","volume":"70","author":"Melikidze","year":"2004","journal-title":"Phys. Rev. B"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"042312","DOI":"10.1103\/PhysRevA.69.042312","article-title":"Mediated entanglement and correlations in a star network of interacting spins","volume":"69","author":"Hutton","year":"2004","journal-title":"Phys. Rev. A"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"062303","DOI":"10.1103\/PhysRevA.96.062303","article-title":"Quantum simulation of quantum channels in nuclear magnetic resonance","volume":"96","author":"Xin","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"013034","DOI":"10.1088\/1367-2630\/11\/1\/013034","article-title":"Randomized benchmarking of single-and multi-qubit control in liquid-state NMR quantum information processing","volume":"11","author":"Ryan","year":"2009","journal-title":"New J. Phys."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1038\/nature05131","article-title":"Bose\u2013Einstein condensation of exciton polaritons","volume":"443","author":"Kasprzak","year":"2006","journal-title":"Nature"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1038\/nature08865","article-title":"A trapped single ion inside a Bose\u2013Einstein condensate","volume":"464","author":"Zipkes","year":"2010","journal-title":"Nature"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"3216","DOI":"10.1364\/OL.30.003216","article-title":"Experimental observation of universality in depolarized light scattering","volume":"30","author":"Puentes","year":"2005","journal-title":"Opt. Lett."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"032319","DOI":"10.1103\/PhysRevA.75.032319","article-title":"Entangled mixed-state generation by twin-photon scattering","volume":"75","author":"Puentes","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"022303","DOI":"10.1103\/PhysRevA.83.022303","article-title":"Realizing controllable depolarization in photonic quantum-information channels","volume":"83","author":"Shaham","year":"2011","journal-title":"Phys. Rev. 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