{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:42:32Z","timestamp":1760168552762,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T00:00:00Z","timestamp":1631059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["Sonata Bis 5 no. 2015\/18\/E\/ST2\/00327","SHENG 1 no. 2018\/30\/Q\/ST2\/00625"],"award-info":[{"award-number":["Sonata Bis 5 no. 2015\/18\/E\/ST2\/00327","SHENG 1 no. 2018\/30\/Q\/ST2\/00625"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001870","name":"Fundacja na rzecz Nauki Polskiej","doi-asserted-by":"publisher","award":["IRAP project, ICTQT, contract no. 2018\/MAB\/5, co-financed by EU via Smart Growth Operational Programme"],"award-info":[{"award-number":["IRAP project, ICTQT, contract no. 2018\/MAB\/5, co-financed by EU via Smart Growth Operational Programme"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We investigate whether the heart rate can be treated as a semi-random source with the aim of amplification by quantum devices. We use a semi-random source model called \u03b5-Santha\u2013Vazirani source, which can be amplified via quantum protocols to obtain a fully private random sequence. We analyze time intervals between consecutive heartbeats obtained from Holter electrocardiogram (ECG) recordings of people of different sex and age. We propose several transformations of the original time series into binary sequences. We have performed different statistical randomness tests and estimated quality parameters. We find that the heart can be treated as a good enough, and private by its nature, source of randomness that every human possesses. As such, in principle, it can be used as input to quantum device-independent randomness amplification protocols. The properly interpreted \u03b5 parameter can potentially serve as a new characteristic of the human heart from the perspective of medicine.<\/jats:p>","DOI":"10.3390\/e23091182","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T10:12:03Z","timestamp":1631095923000},"page":"1182","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Private Weakly-Random Sequences from Human Heart Rate for Quantum Amplification"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8288-3860","authenticated-orcid":false,"given":"Maciej","family":"Stankiewicz","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, Wita Stwosza 57, 80-308 Gda\u0144sk, Poland"},{"name":"International Centre for Theory of Quantum Technologies (ICTQT), University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7540-4147","authenticated-orcid":false,"given":"Karol","family":"Horodecki","sequence":"additional","affiliation":[{"name":"International Centre for Theory of Quantum Technologies (ICTQT), University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"},{"name":"Institute of Informatics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, Wita Stwosza 57, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8667-7474","authenticated-orcid":false,"given":"Omer","family":"Sakarya","sequence":"additional","affiliation":[{"name":"Institute of Informatics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, Wita Stwosza 57, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6014-9577","authenticated-orcid":false,"given":"Danuta","family":"Makowiec","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, Wita Stwosza 57, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124001","DOI":"10.1088\/1361-6633\/aa8731","article-title":"Randomness in quantum mechanics: Philosophy, physics and technology","volume":"80","author":"Bera","year":"2017","journal-title":"Rep. 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