{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:34:59Z","timestamp":1760243699688,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T00:00:00Z","timestamp":1666310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["21-44815L","101017733","IGA-PrF-2022-005"],"award-info":[{"award-number":["21-44815L","101017733","IGA-PrF-2022-005"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"EU H2020 QuantERA II Programme","doi-asserted-by":"publisher","award":["21-44815L","101017733","IGA-PrF-2022-005"],"award-info":[{"award-number":["21-44815L","101017733","IGA-PrF-2022-005"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007059","name":"Palacky University","doi-asserted-by":"publisher","award":["21-44815L","101017733","IGA-PrF-2022-005"],"award-info":[{"award-number":["21-44815L","101017733","IGA-PrF-2022-005"]}],"id":[{"id":"10.13039\/501100007059","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We address minimization of information leakage from continuous-variable quantum channels. It is known, that regime of minimum leakage can be accessible for the modulated signal states with variance equivalent to a shot noise, i.e., vacuum fluctuations, in the case of collective attacks. Here we derive the same condition for the individual attacks and analytically study the properties of the mutual information quantities in and out of this regime. We show that in such regime a joint measurement on the modes of a two-mode entangling cloner, being the optimal individual eavesdropping attack in a noisy Gaussian channel, is no more effective that independent measurements on the modes. Varying variance of the signal out of this regime, we observe the nontrivial statistical effects of either redundancy or synergy between the measurements of two modes of the entangling cloner. The result reveals the non-optimality of entangling cloner individual attack for sub-shot-noise modulated signals. Considering the communication between the cloner modes, we show the advantage of knowing the residual noise after its interaction with the cloner and extend the result to a two-cloner scheme.<\/jats:p>","DOI":"10.3390\/e24101501","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T02:31:03Z","timestamp":1666578663000},"page":"1501","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Redundancy and Synergy of an Entangling Cloner in Continuous-Variable Quantum Communication"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8765-8758","authenticated-orcid":false,"given":"Vladyslav C.","family":"Usenko","sequence":"first","affiliation":[{"name":"Department of Optics, Palacky University, 17. Listopadu 12, 77900 Olomouc, Czech Republic"},{"name":"Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine, Metrolohichna St. 14-b, 03680 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1364\/AOP.361502","article-title":"Advances in quantum cryptography","volume":"12","author":"Pirandola","year":"2020","journal-title":"Adv. Opt. Photon."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TIT.1978.1055892","article-title":"Broadcast channels with confidential messages","volume":"24","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","first-page":"207","article-title":"Distillation of secret key and entanglement from quantum states","volume":"461","author":"Devetak","year":"2005","journal-title":"Proc. R. Soc. A Math. Phys. Eng. 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