{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:56:48Z","timestamp":1760151408530,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,15]],"date-time":"2022-03-15T00:00:00Z","timestamp":1647302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 Research and Innovation Action (Quantum  readout techniques and technologies, QUARTET)","award":["862644"],"award-info":[{"award-number":["862644"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The encoding of classical data in a physical support can be done up to some level of accuracy due to errors and the imperfection of the writing process. Moreover, some degradation of the stored data can happen over time because of physical or chemical instability of the system. Any readout strategy should take into account this natural degree of uncertainty and minimize its effect. An example are optical digital memories, where the information is encoded in two values of reflectance of a collection of cells. Quantum reading using entanglement, has been shown to enhances the readout of an ideal optical memory, where the two level are perfectly characterized. In this work, we analyse the case of imperfect construction of the memory and propose an optimized quantum sensing protocol to maximize the readout accuracy in presence of imprecise writing. The proposed strategy is feasible with current technology and is relatively robust to detection and optical losses. Beside optical memories, this work have implications for identification of pattern in biological system, in spectrophotometry, and whenever the information can be extracted from a transmission\/reflection optical measurement.<\/jats:p>","DOI":"10.3390\/s22062266","type":"journal-article","created":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T03:36:23Z","timestamp":1647401783000},"page":"2266","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Quantum Readout of Imperfect Classical Data"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3288-2875","authenticated-orcid":false,"given":"Giuseppe","family":"Ortolano","sequence":"first","affiliation":[{"name":"Istituto Nazionale di Ricerca Metrologica, Strada Delle Cacce, 10135 Torino, Italy"},{"name":"Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3131-8866","authenticated-orcid":false,"given":"Ivano","family":"Ruo-Berchera","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Ricerca Metrologica, Strada Delle Cacce, 10135 Torino, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1038\/nphoton.2011.35","article-title":"Advances in quantum metrology","volume":"5","author":"Giovannetti","year":"2011","journal-title":"Nat. Photonics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1038\/s41566-018-0301-6","article-title":"Advances in photonic quantum sensing","volume":"12","author":"Pirandola","year":"2018","journal-title":"Nat. Photonics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"024001","DOI":"10.1088\/1681-7575\/aaf7b2","article-title":"Quantum imaging with sub-Poissonian light: Challenges and perspectives in optical metrology","volume":"56","author":"Berchera","year":"2019","journal-title":"Metrologia"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.04.001","article-title":"Squeezed states of light and their applications in laser interferometers","volume":"684","author":"Schnabel","year":"2017","journal-title":"Phys. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1364\/OPTICA.5.000060","article-title":"Deterministic phase measurements exhibiting super-sensitivity and super-resolution","volume":"5","author":"Madsen","year":"2018","journal-title":"Optica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1941010","DOI":"10.1142\/S0219749919410107","article-title":"Quantum enhanced imaging of nonuniform refractive profiles","volume":"17","author":"Ortolano","year":"2019","journal-title":"Int. J. Quantum Inf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"160401","DOI":"10.1103\/PhysRevLett.98.160401","article-title":"Optimal Quantum Estimation of Loss in Bosonic Channels","volume":"98","author":"Monras","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"040305","DOI":"10.1103\/PhysRevA.79.040305","article-title":"Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states","volume":"79","author":"Adesso","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7431","DOI":"10.1038\/s41598-018-25501-w","article-title":"Unbiased estimation of an optical loss at the ultimate quantum limit with twin-beams","volume":"8","author":"Losero","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1038\/nphoton.2010.29","article-title":"Experimental realization of sub-shot-noise quantum imaging","volume":"4","author":"Brida","year":"2010","journal-title":"Nat. Photonics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"073002","DOI":"10.1088\/2040-8978\/18\/7\/073002","article-title":"Real applications of quantum imaging","volume":"18","author":"Genovese","year":"2016","journal-title":"J. Opt."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1038\/nphoton.2013.177","article-title":"Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light","volume":"7","author":"Aasi","year":"2013","journal-title":"Nat. Photonics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"213601","DOI":"10.1103\/PhysRevLett.110.213601","article-title":"Quantum Light in Coupled Interferometers for Quantum Gravity Tests","volume":"110","author":"Degiovanni","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1038\/s42005-020-0368-5","article-title":"Twin beam quantum-enhanced correlated interferometry for testing fundamental physics","volume":"3","author":"Pradyumna","year":"2020","journal-title":"Commun. Phys."},{"key":"ref_16","unstructured":"Helstrom, C. (1976). Quantum Detection and Estimation Theory, Academic Press."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10097","DOI":"10.1088\/0305-4470\/31\/50\/007","article-title":"Quantum state separation, unambiguous discrimination and exact cloning","volume":"31","author":"Chefles","year":"1998","journal-title":"J. Phys. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1126\/science.1160627","article-title":"Enhanced Sensitivity of Photodetection via Quantum Illumination","volume":"321","author":"Lloyd","year":"2008","journal-title":"Science"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"253601","DOI":"10.1103\/PhysRevLett.101.253601","article-title":"Quantum Illumination with Gaussian States","volume":"101","author":"Tan","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"153603","DOI":"10.1103\/PhysRevLett.110.153603","article-title":"Experimental Realization of Quantum Illumination","volume":"110","author":"Lopaeva","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"053808","DOI":"10.1103\/PhysRevA.101.053808","article-title":"Multidimensional quantum-enhanced target detection via spectrotemporal-correlation measurements","volume":"101","author":"Zhang","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"eaay2652","DOI":"10.1126\/sciadv.aay2652","article-title":"Imaging through noise with quantum illumination","volume":"6","author":"Gregory","year":"2020","journal-title":"Sci. Adv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"090504","DOI":"10.1103\/PhysRevLett.106.090504","article-title":"Quantum Reading of a Classical Digital Memory","volume":"106","author":"Pirandola","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"032312","DOI":"10.1103\/PhysRevA.84.032312","article-title":"Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection","volume":"84","author":"Nair","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wilde, M.M., Guha, S., Tan, S., and Lloyd, S. (2012, January 1\u20136). Explicit capacity-achieving receivers for optical communication and quantum reading. Proceedings of the 2012 IEEE International Symposium on Information Theory Proceedings, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6284251"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1241010","DOI":"10.1142\/S0219749912410109","article-title":"Ideal quantum reading of optical memories","volume":"10","author":"Bisio","year":"2012","journal-title":"Int. J. Quantum Inf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"012308","DOI":"10.1103\/PhysRevA.85.012308","article-title":"Experimental implementation of unambiguous quantum reading","volume":"85","author":"Bisio","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1515\/qmetro-2017-0009","article-title":"Error Free Quantum Reading by Quasi Bell State of Entangled Coherent States","volume":"4","author":"Hirota","year":"2017","journal-title":"Quantum Meas. Quantum Metrol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Fernandes Pereira, F.R., and Mancini, S. (2022). Error Probability Mitigation in Quantum Reading Using Classical Codes. Entropy, 24.","DOI":"10.3390\/e24010005"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"eabc7796","DOI":"10.1126\/sciadv.abc7796","article-title":"Experimental quantum reading with photon counting","volume":"7","author":"Ortolano","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"113012","DOI":"10.1088\/1367-2630\/13\/11\/113012","article-title":"Quantum reading capacity","volume":"13","author":"Pirandola","year":"2011","journal-title":"New J. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1038\/s42005-020-0369-4","article-title":"Entanglement-enhanced testing of multiple quantum hypotheses","volume":"3","author":"Zhuang","year":"2020","journal-title":"Commun. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2150012","DOI":"10.1142\/S0129055X21500124","article-title":"Classical capacities of memoryless but not identical quantum channels","volume":"33","author":"Oskouei","year":"2021","journal-title":"Rev. Math. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Revson, F., and Mancini, S. (2021, January 12\u201320). Polar Codes for Quantum Reading. Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia.","DOI":"10.1109\/ISIT45174.2021.9517807"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"eabm3093","DOI":"10.1126\/sciadv.abm3093","article-title":"Quantum conformance test","volume":"7","author":"Ortolano","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_36","first-page":"177","article-title":"Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel","volume":"9","author":"Holevo","year":"1973","journal-title":"Probl. Inform. Transm."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/18.651037","article-title":"The capacity of the quantum channel with general signal states","volume":"44","author":"Holevo","year":"1998","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1103\/PhysRevA.54.1869","article-title":"Classical information capacity of a quantum channel","volume":"54","author":"Hausladen","year":"1996","journal-title":"Phys. Rev. A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1038\/s41534-019-0162-y","article-title":"Fundamental limits to quantum channel discrimination","volume":"5","author":"Pirandola","year":"2019","journal-title":"NPJ Quantum Inf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"080505","DOI":"10.1103\/PhysRevLett.125.080505","article-title":"Ultimate Limits for Multiple Quantum Channel Discrimination","volume":"125","author":"Zhuang","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Holevo, A.S. (2012). Quantum Systems, Channels, Information: A Mathematical Introduction, De Gruyter.","DOI":"10.1515\/9783110273403"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1103\/RevModPhys.77.513","article-title":"Quantum information with continuous variables","volume":"77","author":"Braunstein","year":"2005","journal-title":"Rev. Mod. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1103\/RevModPhys.84.621","article-title":"Gaussian quantum information","volume":"84","author":"Weedbrook","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"013833","DOI":"10.1103\/PhysRevA.76.013833","article-title":"Sub-shot-noise photon-number correlation in a mesoscopic twin beam of light","volume":"76","author":"Bondani","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1364\/OL.41.001841","article-title":"Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime","volume":"41","author":"Avella","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"094002","DOI":"10.1088\/2040-8986\/aa7b27","article-title":"Photon-number correlation for quantum enhanced imaging and sensing","volume":"19","author":"Meda","year":"2017","journal-title":"J. Opt."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., and Chuang, I.L. (2011). Quantum Computation and Quantum Information, Cambridge University Press. [10th ed.].","DOI":"10.1017\/CBO9780511976667"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"180502","DOI":"10.1103\/PhysRevLett.125.180502","article-title":"Entanglement-assisted absorption spectroscopy","volume":"125","author":"Shi","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"15008","DOI":"10.1038\/npjqi.2015.8","article-title":"Entropy generation in Gaussian quantum transformations: Applying the replica method to continuous-variable quantum information theory","volume":"2","author":"Gagatsos","year":"2016","journal-title":"npj Quantum Inf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2266\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:36:53Z","timestamp":1760135813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2266"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,15]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["s22062266"],"URL":"https:\/\/doi.org\/10.3390\/s22062266","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,3,15]]}}}