{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:18Z","timestamp":1760057838007,"version":"build-2065373602"},"reference-count":94,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,23]],"date-time":"2025-02-23T00:00:00Z","timestamp":1740268800000},"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>In this paper, we investigate the interference engineering of the open quantum system, where the environment is made indefinite either through the use of an interferometer or the introduction of auxiliary qubits. The environments are modeled by fully connected qubit baths with exact analytical dynamics. As the system passes through the interferometer or is controlled by auxiliary qubits, it is propagated along different paths or their superpositions, leading to distinct interactions with the environment in each path. This results in the superposition of the environments, which can be detected through specific measurements that retain certain coherent information about the paths. Our results demonstrate that the indefiniteness of the environment can significantly enhance the quantum correlations. However, only the statistical mixture of the influences from the environments is preserve provided that the path coherence is destructed. We also examine the serviceability of the indefiniteness as a resource for teleportation and quantum parameter estimation. Additionally, we discuss how to quantify the indefiniteness and the ways in which it affects the system\u2019s dynamics from the perspective of wave\u2013particle-entanglement-ignorance complementarity. Our study highlights the potential benefits of an indefinite environment in quantum information processing and sheds light on the fundamental principles underlying its effects.<\/jats:p>","DOI":"10.3390\/e27030228","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T06:47:17Z","timestamp":1740379637000},"page":"228","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Open Quantum System Interacting with an Interference Engineering Environment"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3270-8700","authenticated-orcid":false,"given":"He","family":"Wang","sequence":"first","affiliation":[{"name":"College of Physics, Jilin University, Changchun 130021, China"},{"name":"State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Changchun 130021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Stony Brook University, Stony Brook, NY 11794-3400, USA"},{"name":"Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3400, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,23]]},"reference":[{"key":"ref_1","unstructured":"Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1080\/00107514.2019.1667078","article-title":"Quantum error correction: An introductory guide","volume":"60","author":"Roffe","year":"2019","journal-title":"Contemp. Phys."},{"key":"ref_3","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_4","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_5","first-page":"295","article-title":"Review of decoherence free subspaces, noiseless subsystems, and dynamical decoupling","volume":"154","author":"Lidar","year":"2014","journal-title":"Adv. Chem. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3520","DOI":"10.1103\/PhysRevLett.85.3520","article-title":"Dynamical Generation of Noiseless Quantum Subsystems","volume":"85","author":"Viola","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"050501","DOI":"10.1103\/PhysRevLett.96.050501","article-title":"Method to Find Quantum Noiseless Subsystems","volume":"96","author":"Choi","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1103\/PhysRevA.49.2133","article-title":"Quantum theory of continuous feedback","volume":"49","author":"Wiseman","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"012105","DOI":"10.1103\/PhysRevA.62.012105","article-title":"Quantum feedback control and classical control theory","volume":"62","author":"Doherty","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.02.003","article-title":"Quantum feedback: Theory, experiments, and applications","volume":"679","author":"Zhang","year":"2017","journal-title":"Phys. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2417","DOI":"10.1103\/PhysRevLett.82.2417","article-title":"Dynamical Decoupling of Open Quantum Systems","volume":"82","author":"Viola","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.1103\/PhysRevA.41.2295","article-title":"Quantum Zeno effect","volume":"41","author":"Itano","year":"1990","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"080401","DOI":"10.1103\/PhysRevLett.89.080401","article-title":"Quantum Zeno Subspaces","volume":"89","author":"Facchi","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.physrep.2005.03.001","article-title":"Quantum Zeno effect by general measurements","volume":"412","author":"Koshino","year":"2005","journal-title":"Phys. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"012101","DOI":"10.1103\/PhysRevA.90.012101","article-title":"Zeno and anti-Zeno effects on dephasing","volume":"90","author":"Chaudhry","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chaudhry, A.Z. (2016). A general framework for the quantum Zeno and anti-Zeno effects. Sci. Rep., 6.","DOI":"10.1038\/srep29497"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"052122","DOI":"10.1103\/PhysRevA.91.052122","article-title":"Floquet control of quantum dissipation in spin chains","volume":"91","author":"Chen","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"013007","DOI":"10.1088\/1367-2630\/aaf8f4","article-title":"Floquet engineering to entanglement protection of distant nitrogen vacancy centers","volume":"21","author":"Yang","year":"2019","journal-title":"New J. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"060201","DOI":"10.1103\/PhysRevA.102.060201","article-title":"Floquet engineering to reactivate a dissipative quantum battery","volume":"102","author":"Bai","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, H., and Wang, J. (2023). Entanglement and work statistics in the driven open system. arXiv.","DOI":"10.1007\/s11128-024-04464-0"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1038\/s41467-025-56242-w","article-title":"Non-Markovian quantum exceptional points","volume":"16","author":"Lin","year":"2025","journal-title":"Nat. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1007\/s11128-021-03277-9","article-title":"The effect of nonequilibrium entropy production on the quantum Fisher information and correlations","volume":"21","author":"Wang","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"052404","DOI":"10.1103\/PhysRevA.106.052404","article-title":"Quantum correlations of a two-qubit system and the Aubry-Andr\u00e9 chain in bosonic environments","volume":"106","author":"Wang","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s11128-021-03086-0","article-title":"Entanglement versus Bell nonlocality of quantum nonequilibrium steady states","volume":"20","author":"Zhang","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"052331","DOI":"10.1103\/PhysRevA.100.052331","article-title":"Nonequilibrium effects on quantum correlations: Discord, mutual information, and entanglement of a two-fermionic system in bosonic and fermionic environments","volume":"100","author":"Wang","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"042320","DOI":"10.1103\/PhysRevA.99.042320","article-title":"Steady-state entanglement and coherence of two coupled qubits in equilibrium and nonequilibrium environments","volume":"99","author":"Wang","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"093021","DOI":"10.1088\/1367-2630\/17\/9\/093021","article-title":"Shape, orientation and magnitude of the curl quantum flux, the coherence and the statistical correlations in energy transport at nonequilibrium steady state","volume":"17","author":"Zhang","year":"2015","journal-title":"New J. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1103\/PhysRevA.59.2468","article-title":"Cavity Loss Induced Generation of Entangled Atoms","volume":"59","author":"Plenio","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"042307","DOI":"10.1103\/PhysRevA.78.042307","article-title":"Preparation of entangled states by quantum Markov processes","volume":"78","author":"Kraus","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1038\/nphys1342","article-title":"Quantum computation and quantum-state engineering driven by dissipation","volume":"5","author":"Verstraete","year":"2009","journal-title":"Nat. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"040301","DOI":"10.1103\/PhysRevA.86.040301","article-title":"Perfect discrimination of no-signalling channels via quantum superposition of causal structures","volume":"86","author":"Chiribella","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"042124","DOI":"10.1103\/PhysRevA.92.042124","article-title":"Information-theoretic constraints on correlations with indefinite causal order","volume":"92","author":"Ibnouhsein","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"120502","DOI":"10.1103\/PhysRevLett.120.120502","article-title":"Enhanced communication with the assistance of indefinite causal order","volume":"120","author":"Ebler","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"090503","DOI":"10.1103\/PhysRevLett.121.090503","article-title":"Indefinite causal order in a quantum switch","volume":"121","author":"Goswami","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"012340","DOI":"10.1103\/PhysRevA.101.012340","article-title":"Channel capacity enhancement with indefinite causal order","volume":"101","author":"Loizeau","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"105003","DOI":"10.1088\/2399-6528\/abbd77","article-title":"Superposition of causal order enables perfect quantum teleportation with very noisy singlets","volume":"4","author":"Mukhopadhyay","year":"2020","journal-title":"J. Phys. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"012024","DOI":"10.1088\/1742-6596\/1540\/1\/012024","article-title":"Featuring causal order in teleportation of two quantum teleportation channels","volume":"1540","author":"Delgado","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_38","unstructured":"Mukhopadhyay, C., Gupta, M.K., and Pati, A.K. (2018). Superposition of causal order as a metrological resource for quantum thermometry. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"032615","DOI":"10.1103\/PhysRevA.103.032615","article-title":"Noisy quantum metrology with the assistance of indefinite causal order","volume":"103","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"032214","DOI":"10.1103\/PhysRevA.104.032214","article-title":"Quantum parameter estimation on coherently superposed noisy channel","volume":"104","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_41","first-page":"128300","article-title":"Indefinite causal order for quantum metrology with quantum thermal noise","volume":"447","year":"2021","journal-title":"Phys. Lett. A"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"190503","DOI":"10.1103\/PhysRevLett.124.190503","article-title":"Quantum metrology with indefinite causal order","volume":"124","author":"Zhao","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"128749","DOI":"10.1016\/j.physleta.2023.128749","article-title":"Quantum Fisher information of phase estimation in the presence of indefinite causal order","volume":"468","author":"Ban","year":"2023","journal-title":"Phys. Lett. A"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"070603","DOI":"10.1103\/PhysRevLett.125.070603","article-title":"Quantum Refrigeration with Indefinite Causal Order","volume":"125","author":"Felce","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"100603","DOI":"10.1103\/PhysRevLett.129.100603","article-title":"Experimental Realization of a Quantum Refrigerator Driven by Indefinite Causal Orders","volume":"129","author":"Nie","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"032223","DOI":"10.1103\/PhysRevA.103.032223","article-title":"Interferometric approach to open quantum systems and non-Markovian dynamics","volume":"103","author":"Siltanen","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"033143","DOI":"10.1103\/PhysRevResearch.4.033143","article-title":"Space-time dual quantum Zeno effect: Interferometric engineering of open quantum system dynamics","volume":"4","author":"Lin","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Lin, J.-D., and Chen, Y.-N. (2023). Boosting entanglement growth of many-body localization by superpositions of disorder. arXiv.","DOI":"10.1103\/PhysRevA.108.022203"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s11128-020-02856-6","article-title":"Relaxation process of a two-level system in a coherent superposition of two environments","volume":"19","author":"Ban","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s11128-020-02903-2","article-title":"Decoherence of a two-level system in a coherent superposition of two dephasing environments","volume":"19","author":"Ban","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"126936","DOI":"10.1016\/j.physleta.2020.126936","article-title":"Two-qubit correlation in two independent environments with indefiniteness","volume":"385","author":"Ban","year":"2021","journal-title":"Phys. Lett. A"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s11128-021-03369-6","article-title":"Temporal steering of a two-level system interacting with a coherent superposition of two environments","volume":"21","author":"Ban","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s11128-022-03578-7","article-title":"Quantum correlations of two qubits indefinitely interacting with dephasing environments","volume":"21","author":"Ban","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_54","unstructured":"Wood, C.E., Verma, H., Costa, F., and Zych, M. (2021). Operational models of temperature superpositions. arXiv."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"043007","DOI":"10.1088\/1367-2630\/aab2f9","article-title":"Mixing-induced quantum non-Markovianity and information flow","volume":"20","author":"Breuer","year":"2018","journal-title":"New J. Phys."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"045331","DOI":"10.1103\/PhysRevB.75.045331","article-title":"Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment","volume":"75","author":"Yuan","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Wu, W., and Wang, J. (2020). Wave\u2013Particle\u2013Entanglement\u2013Ignorance Complementarity for General Bipartite Systems. Entropy, 22.","DOI":"10.3390\/e22080813"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1007\/s11128-012-0432-5","article-title":"Quantum walks: A comprehensive review","volume":"11","year":"2012","journal-title":"Quantum Inf. Process."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1103\/RevModPhys.85.79","article-title":"Nuclear spin physics in quantum dots: An optical investigation","volume":"85","author":"Urbaszek","year":"2013","journal-title":"Rev. Mod. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"144306","DOI":"10.1103\/PhysRevB.95.144306","article-title":"Nonequilibrium-induced enhancement of dynamical quantum coherence and entanglement of spin arrays","volume":"95","author":"Zhang","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"2743","DOI":"10.1016\/j.physleta.2014.07.042","article-title":"Entanglement and quantum phase transition of spin glass: A renormalization group approach","volume":"378","author":"Koh","year":"2014","journal-title":"Phys. lett. A"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"113020","DOI":"10.1088\/1367-2630\/10\/11\/113020","article-title":"Fully connected network of superconducting qubits in a cavity","volume":"10","author":"Tsomokos","year":"2008","journal-title":"New J. Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"012021","DOI":"10.1088\/1742-6596\/387\/1\/012021","article-title":"Quantum phase transitions in the LMG model by means of quantum information concepts","volume":"387","author":"Hirsch","year":"2012","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"eaba4935","DOI":"10.1126\/sciadv.aba4935","article-title":"Probing dynamical phase transitions with a superconducting quantum simulator","volume":"6","author":"Xu","year":"2020","journal-title":"Sci. Adv."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"024113","DOI":"10.1103\/PhysRevE.107.024113","article-title":"Finite-size criticality in fully connected spin models on superconducting quantum hardware","volume":"107","author":"Grossi","year":"2023","journal-title":"Phys. Rev. E"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"130503","DOI":"10.1103\/PhysRevLett.97.130503","article-title":"Quantum Pattern Retrieval by Qubit Networks with Hebb Interactions","volume":"77","author":"Diamantini","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"115301","DOI":"10.1088\/1751-8121\/aaabcb","article-title":"Open quantum generalisation of Hopfield neural networks","volume":"51","author":"Rotondo","year":"2018","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"214307","DOI":"10.1103\/PhysRevB.95.214307","article-title":"Floquet time crystal in the Lipkin-Meshkov-Glick model","volume":"95","author":"Russomanno","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"014307","DOI":"10.1103\/PhysRevB.104.014307","article-title":"Symmetries and conserved quantities of boundary time crystals in generalized spin models","volume":"104","author":"Piccitto","year":"2021","journal-title":"Phys. Rev. B"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Wang, H., and Wang, J. (2023). The time crystal phase emerges from the qubit network under unitary random operations. arXiv.","DOI":"10.1103\/PhysRevA.108.012209"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1140\/epjd\/e2010-00065-0","article-title":"Non-Markovian entanglement dynamics of two spin-1\/2 particles embedded in two separate spin star baths with tunable external magnetic fields","volume":"57","author":"Xiao","year":"2010","journal-title":"Eur. Phys. J. D"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"052125","DOI":"10.1103\/PhysRevA.96.052125","article-title":"Dynamics and thermodynamics of a central spin immersed in a spin bath","volume":"96","author":"Mukhopadhyay","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"55","DOI":"10.12743\/quanta.v10i1.162","article-title":"Revisiting the Quantum Open System Dynamics of Central Spin Model","volume":"10","author":"Bhattacharya","year":"2021","journal-title":"Quanta"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"032435","DOI":"10.1103\/PhysRevA.106.032435","article-title":"Dynamics of two central spins immersed in spin baths","volume":"106","author":"Tiwari","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"2200452","DOI":"10.1002\/andp.202200452","article-title":"Quantum Correlations and Speed Limit of Central Spin Systems","volume":"535","author":"Tiwari","year":"2023","journal-title":"Ann. Phys."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"095024","DOI":"10.1088\/1367-2630\/14\/9\/095024","article-title":"Quantum simulation of spin models on an arbitrary lattice with trapped ions","volume":"14","author":"Korenblit","year":"2012","journal-title":"New J. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"025001","DOI":"10.1103\/RevModPhys.93.025001","article-title":"Programmable quantum simulations of spin systems with trapped ions","volume":"93","author":"Monroe","year":"2021","journal-title":"Rev. Mod. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1103\/PhysRev.58.1098","article-title":"Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet","volume":"58","author":"Holstein","year":"1940","journal-title":"Phys. Rev."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"140401","DOI":"10.1103\/PhysRevLett.113.140401","article-title":"Quantifying Coherence","volume":"113","author":"Cramer","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","article-title":"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels","volume":"70","author":"Bennett","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1103\/PhysRevLett.67.661","article-title":"Quantum Cryptography Based on Bell\u2019s Theorem","volume":"67","author":"Ekert","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"040505","DOI":"10.1103\/PhysRevLett.93.040505","article-title":"Quantum Dense Coding with Atomic Qubits","volume":"93","author":"Schaetz","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_83","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_84","doi-asserted-by":"crossref","first-page":"5022","DOI":"10.1103\/PhysRevLett.78.5022","article-title":"Entanglement of a Pair of Quantum Bits","volume":"78","author":"Hill","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"017901","DOI":"10.1103\/PhysRevLett.88.017901","article-title":"Quantum Discord: A Measure of the Quantumness of Correlations","volume":"88","author":"Ollivier","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"4649","DOI":"10.1103\/PhysRevLett.105.190502","article-title":"Necessary and Sufficient Condition for Nonzero Quantum Discord","volume":"105","author":"Dakic","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0375-9601(96)00639-1","article-title":"Teleportation, Bell\u2019s inequalities and inseparability","volume":"222","author":"Horodecki","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_88","first-page":"797","article-title":"Bell\u2019s inequalities versus teleportation: What is nonlocality?","volume":"72","author":"Popescu","year":"1994","journal-title":"Phys. Rev. A"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"035006","DOI":"10.1103\/RevModPhys.90.035006","article-title":"Quantum-enhanced measurements without entanglement","volume":"90","author":"Braun","year":"2018","journal-title":"Rev. Mod. Phys."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"035005","DOI":"10.1103\/RevModPhys.90.035005","article-title":"Quantum metrology with nonclassical states of atomic ensembles","volume":"90","author":"Smerzi","year":"2018","journal-title":"Rev. Mod. Phys."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"022321","DOI":"10.1103\/PhysRevA.85.022321","article-title":"Fisher information and multiparticle entanglement","volume":"85","author":"Hyllus","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1103\/PhysRevD.19.473","article-title":"Complementarity in the double-slit experiment: Quantum nonseparability and a quantitive statement of Bohr\u2019s principle","volume":"19","author":"Wootters","year":"1979","journal-title":"Phys. Rev. D"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1016\/j.optcom.2009.10.044","article-title":"Quantitative complementarity relations in bipartite systems: Entanglement as a physical reality","volume":"283","author":"Jakob","year":"2010","journal-title":"Opt. Commun."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10702-005-3956-4","article-title":"Complementarity relations for multi-qubit systems","volume":"18","author":"Tessier","year":"2005","journal-title":"Found. Phys. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/228\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:40:50Z","timestamp":1760028050000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,23]]},"references-count":94,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["e27030228"],"URL":"https:\/\/doi.org\/10.3390\/e27030228","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,2,23]]}}}