{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:00:26Z","timestamp":1775167226333,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T00:00:00Z","timestamp":1581292800000},"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":["2015\/19\/B\/ST2\/02856"],"award-info":[{"award-number":["2015\/19\/B\/ST2\/02856"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We investigate advantages and disadvantages of using Gazeau\u2013Klauder coherent states for optical communication. In this short paper we show that using an alphabet consisting of coherent Gazeau\u2013Klauder states related to a Kerr-type nonlinear oscillator instead of standard Perelomov coherent states results in lowering of the Helstrom bound for error probability in binary communication. We also discuss trace distance between Gazeau\u2013Klauder coherent states and a standard coherent state as a quantifier of distinguishability of alphabets.<\/jats:p>","DOI":"10.3390\/e22020201","type":"journal-article","created":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T09:25:21Z","timestamp":1581413121000},"page":"201","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Binary Communication with Gazeau\u2013Klauder Coherent States"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4912-4859","authenticated-orcid":false,"given":"Jerzy","family":"Dajka","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Silesia in Katowice, 40-007 Katowice, Poland"},{"name":"Institute of Computer Science, University of Silesia in Katowice, 40-007 Katowice, Poland"},{"name":"Silesian Center for Education and Interdisciplinary Research, University of Silesia in Katowice, 40-007 Chorz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2296-4532","authenticated-orcid":false,"given":"Jerzy","family":"\u0141uczka","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Silesia in Katowice, 40-007 Katowice, Poland"},{"name":"Silesian Center for Education and Interdisciplinary Research, University of Silesia in Katowice, 40-007 Chorz\u00f3w, Poland"},{"name":"Institute of Mathematics, University of Silesia in Katowice, 40-007 Katowice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Akira Furusawa, A., and van Loock, P. (2011). Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing, Wiley.","DOI":"10.1002\/9783527635283"},{"key":"ref_2","first-page":"431","article-title":"Security of Quantum Key Distribution Using Weak Coherent States with Nonrandom Phases","volume":"7","author":"Lo","year":"2007","journal-title":"Quantum Inf. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"042319","DOI":"10.1103\/PhysRevA.68.042319","article-title":"Quantum computation with optical coherent states","volume":"68","author":"Ralph","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"012013","DOI":"10.1088\/1742-6596\/213\/1\/012013","article-title":"Coherent states in Quantum Information: An example of experimental manipulations","volume":"213","author":"Gazeau","year":"2010","journal-title":"J. Phys. Conf. 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