{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T01:25:12Z","timestamp":1778721912755,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T00:00:00Z","timestamp":1732147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["1240843"],"award-info":[{"award-number":["1240843"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["1231826"],"award-info":[{"award-number":["1231826"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["1230796"],"award-info":[{"award-number":["1230796"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["1240746"],"award-info":[{"award-number":["1240746"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["11221231"],"award-info":[{"award-number":["11221231"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["ID22I10262"],"award-info":[{"award-number":["ID22I10262"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["ICN17012"],"award-info":[{"award-number":["ICN17012"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["ING222010004"],"award-info":[{"award-number":["ING222010004"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (ANID)","doi-asserted-by":"publisher","award":["INCA210005"],"award-info":[{"award-number":["INCA210005"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["1240843"],"award-info":[{"award-number":["1240843"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["1231826"],"award-info":[{"award-number":["1231826"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["1230796"],"award-info":[{"award-number":["1230796"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["1240746"],"award-info":[{"award-number":["1240746"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["11221231"],"award-info":[{"award-number":["11221231"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["ID22I10262"],"award-info":[{"award-number":["ID22I10262"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["ICN17012"],"award-info":[{"award-number":["ICN17012"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["ING222010004"],"award-info":[{"award-number":["ING222010004"]}]},{"name":"ANID\u2014Millennium Science Initiative Program","award":["INCA210005"],"award-info":[{"award-number":["INCA210005"]}]},{"name":"Ingenier\u00eda 2030","award":["1240843"],"award-info":[{"award-number":["1240843"]}]},{"name":"Ingenier\u00eda 2030","award":["1231826"],"award-info":[{"award-number":["1231826"]}]},{"name":"Ingenier\u00eda 2030","award":["1230796"],"award-info":[{"award-number":["1230796"]}]},{"name":"Ingenier\u00eda 2030","award":["1240746"],"award-info":[{"award-number":["1240746"]}]},{"name":"Ingenier\u00eda 2030","award":["11221231"],"award-info":[{"award-number":["11221231"]}]},{"name":"Ingenier\u00eda 2030","award":["ID22I10262"],"award-info":[{"award-number":["ID22I10262"]}]},{"name":"Ingenier\u00eda 2030","award":["ICN17012"],"award-info":[{"award-number":["ICN17012"]}]},{"name":"Ingenier\u00eda 2030","award":["ING222010004"],"award-info":[{"award-number":["ING222010004"]}]},{"name":"Ingenier\u00eda 2030","award":["INCA210005"],"award-info":[{"award-number":["INCA210005"]}]},{"name":"InES Ciencia Abierta","award":["1240843"],"award-info":[{"award-number":["1240843"]}]},{"name":"InES Ciencia Abierta","award":["1231826"],"award-info":[{"award-number":["1231826"]}]},{"name":"InES Ciencia Abierta","award":["1230796"],"award-info":[{"award-number":["1230796"]}]},{"name":"InES Ciencia Abierta","award":["1240746"],"award-info":[{"award-number":["1240746"]}]},{"name":"InES Ciencia Abierta","award":["11221231"],"award-info":[{"award-number":["11221231"]}]},{"name":"InES Ciencia Abierta","award":["ID22I10262"],"award-info":[{"award-number":["ID22I10262"]}]},{"name":"InES Ciencia Abierta","award":["ICN17012"],"award-info":[{"award-number":["ICN17012"]}]},{"name":"InES Ciencia Abierta","award":["ING222010004"],"award-info":[{"award-number":["ING222010004"]}]},{"name":"InES Ciencia Abierta","award":["INCA210005"],"award-info":[{"award-number":["INCA210005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Fiber-optic Mach\u2013Zehnder interferometers are widely used in research areas such as telecommunications, spectroscopy, and quantum information. These optical structures are known to be affected by phase fluctuations that are usually modeled as multiparametric noise. This multidimensional noise must be stabilized or compensated for to enable fiber-optic Mach\u2013Zehnder architectures for practical applications. In this work, we study the effectiveness of a modified Perturb-and-Observe (P&amp;O) algorithm to control multidimensional phase noise in fiber-based multi-arm Mach\u2013Zehnder interferometers. We demonstrate the feasibility of stabilizing multidimensional phase noise by numerical simulations using a simple feedback control scheme and analyze the algorithm\u2019s performance for systems up to dimension 8\u00d78. We achieved minimal steady-state errors that guarantee high optical visibility in complex optical systems with N\u00d7N matrices (with N=[2,3,4,5,6,7,8]).<\/jats:p>","DOI":"10.3390\/a17120534","type":"journal-article","created":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T06:11:54Z","timestamp":1732169514000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Adaptive-Step Perturb-and-Observe Algorithm for Multidimensional Phase Noise Stabilization in Fiber-Based Multi-Arm Mach\u2013Zehnder Interferometers"],"prefix":"10.3390","volume":"17","author":[{"given":"H.","family":"Abarz\u00faa","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Concepci\u00f3n 4090541, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3149-1120","authenticated-orcid":false,"given":"C.","family":"Melo","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad de Concepci\u00f3n, Concepci\u00f3n 4070411, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. E.","family":"Restrepo","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Concepci\u00f3n 4090541, Chile"},{"name":"Centro de Energ\u00eda, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Concepci\u00f3n 4090541, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Vergara","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Concepci\u00f3n 4090541, Chile"},{"name":"Centro de Energ\u00eda, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Concepci\u00f3n 4090541, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0386-1055","authenticated-orcid":false,"given":"D.","family":"Sbarbaro","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad de Concepci\u00f3n, Concepci\u00f3n 4070411, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9357-8025","authenticated-orcid":false,"given":"G.","family":"Ca\u00f1as","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad del B\u00edo-B\u00edo, Concepci\u00f3n 4081112, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Lima","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Concepci\u00f3n, Concepci\u00f3n 4070411, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Saavedra","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad de Concepci\u00f3n, Concepci\u00f3n 4070411, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6232-6012","authenticated-orcid":false,"given":"J.","family":"Cari\u00f1e","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad Cat\u00f3lica de la Sant\u00edsima Concepci\u00f3n, Concepci\u00f3n 4090541, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2699","DOI":"10.1002\/adpr.202100371","article-title":"Optical Fiber Sensors: Working Principle, Applications, and Limitations","volume":"3","author":"Elsherif","year":"2022","journal-title":"Adv. Photonics Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11109","DOI":"10.1364\/OE.20.011109","article-title":"All-fiber Mach-Zehnder interferometers for sensing applications","volume":"20","author":"Li","year":"2012","journal-title":"Opt. Express"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4469","DOI":"10.1364\/OE.14.004469","article-title":"High-speed optical DQPSK and FSK modulation using integrated Mach-Zehnder interferometers","volume":"14","author":"Kawanishi","year":"2006","journal-title":"Opt. Express"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","article-title":"Quantum Cryptography","volume":"74","author":"Gisin","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2871","DOI":"10.1038\/ncomms3871","article-title":"Long-distance distribution of genuine energy-time entanglement","volume":"4","author":"Cuevas","year":"2013","journal-title":"Nat. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"190401","DOI":"10.1103\/PhysRevLett.121.190401","article-title":"Postselection-Loophole-Free Bell Violation with Genuine Time-Bin Entanglement","volume":"121","author":"Vedovato","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2530","DOI":"10.1364\/OL.39.002530","article-title":"Active stabilization of a Michelson interferometer at an arbitrary phase with subnanometer resolution","volume":"39","author":"Grassani","year":"2014","journal-title":"Opt. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1764","DOI":"10.1364\/OL.36.001764","article-title":"Stable single-photon interference in a 1 km fiber-optic Mach\u2013Zehnder interferometer with continuous phase adjustment","volume":"36","author":"Xavier","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"030503","DOI":"10.1103\/PhysRevLett.115.030503","article-title":"Postselection-Loophole-Free Bell Test Over an Installed Optical Fiber Network","volume":"115","author":"Carvacho","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1126\/science.1104149","article-title":"Quantum-enhanced measurements: Beating the standard quantum limit","volume":"306","author":"Giovannetti","year":"2004","journal-title":"Science"},{"key":"ref_11","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1038\/nphys1150","article-title":"Simplifying quantum logic using higher-dimensional Hilbert spaces","volume":"5","author":"Lanyon","year":"2009","journal-title":"Nat. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"127902","DOI":"10.1103\/PhysRevLett.88.127902","article-title":"Security of quantum key distribution using d-level systems","volume":"88","author":"Cerf","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1103\/RevModPhys.81.1301","article-title":"The security of practical quantum key distribution","volume":"81","author":"Scarani","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"022317","DOI":"10.1103\/PhysRevA.96.022317","article-title":"High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers","volume":"96","author":"Vera","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/s41534-017-0026-2","article-title":"High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits","volume":"3","author":"Ding","year":"2017","journal-title":"NPJ Quantum Inf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4302","DOI":"10.1038\/s41598-017-04444-8","article-title":"Experimental Demonstration of Four-Dimensional Photonic Spatial Entanglement between Multi-Core Optical Fibres","volume":"7","author":"Lee","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"034024","DOI":"10.1103\/PhysRevApplied.15.034024","article-title":"Multidimensional Entanglement Generation with Multicore Optical Fibers","volume":"15","author":"Gomez","year":"2021","journal-title":"Phys. Rev. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7800908","DOI":"10.1109\/JPHOT.2016.2516254","article-title":"Spatial-division multiplexed Mach\u2013Zehnder interferometers in heterogeneous multicore fiber for multidimensional measurement","volume":"8","author":"Gan","year":"2016","journal-title":"IEEE Photonics J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2793","DOI":"10.1364\/JOSAB.36.002793","article-title":"Phase and polarization autocompensating N-dimensional quantum cryptography in multicore optical fibers","volume":"36","author":"Balado","year":"2019","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1038\/s41534-021-00398-y","article-title":"Path-encoded high-dimensional quantum communication over a 2-km multicore fiber","volume":"7","author":"Cozzolino","year":"2021","journal-title":"NPJ Quantum Inf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1364\/OPTICA.388912","article-title":"Multi-core fiber integrated multi-port beam splitters for quantum information processing","volume":"7","author":"Skrzypczyk","year":"2020","journal-title":"Optica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"010320","DOI":"10.1103\/PRXQuantum.2.010320","article-title":"Computational advantage from the quantum superposition of multiple temporal orders of photonic gates","volume":"2","author":"Taddei","year":"2021","journal-title":"PRX Quantum"},{"key":"ref_24","first-page":"379","article-title":"A Comprehensive Review of Maximum Power Point Tracking Techniques for Photovoltaic Systems","volume":"112","author":"Yatinkumar","year":"2020","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TSTE.2011.2168245","article-title":"Assessment of Perturb and Observe MPPT Algorithm Implementation Techniques for PV Pumping Applications","volume":"3","author":"Elgendy","year":"2012","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/TEC.2006.874230","article-title":"Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques","volume":"22","author":"Esram","year":"2007","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1473","DOI":"10.1109\/LPT.2020.3036093","article-title":"A MZ Modulator Bias Control System Based on Variable Step P&O Algorithm","volume":"32","author":"Ji","year":"2020","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_28","first-page":"111","article-title":"Nonclassical statistics at multiport beam-splitters","volume":"60","author":"Mattle","year":"1995","journal-title":"Appl. Phys.-Lasers Opt."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1364\/OL.21.000302","article-title":"All-fiber three-path mach-zehnder interferometer","volume":"21","author":"Weihs","year":"1996","journal-title":"Opt. Lett."},{"key":"ref_30","unstructured":"Thorlabs, Inc (2024, October 01). Available online: https:\/\/www.thorlabs.com\/."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/978-94-007-2033-6_12","article-title":"Controllability and Observability. Vibration Control of Active Structures","volume":"Volume 179","author":"Preumont","year":"2011","journal-title":"Solid Mechanics and Its Applications"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/12\/534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:36:30Z","timestamp":1760114190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/12\/534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,21]]},"references-count":31,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["a17120534"],"URL":"https:\/\/doi.org\/10.3390\/a17120534","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,21]]}}}