Inverse Laplace and Mellin integral transforms modified for use in quantum communications

Quantum Physics [Submitted on 9 Apr 2026] Inverse Laplace and Mellin integral transforms modified for use in quantum communications Gustavo Alvarez, Igor Kondrashuk Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum chromodynamics, in which the optic theorem and the renormalization group equation can be solved by a unique contour integral written in two different "dual" ways related between themselves by a complex map in the complex plane of Mellin variable. The inverse integral transformation should be modified to be applied for these contour integral solutions. These modified inverse transformations may be used in security protocols for quantum computers. Here we do a brief review of the basic integral transforms and propose their modification for the extended domains. Comments: 13 pages, 4 figures Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) MSC classes: 44A15, 44A20, 81T13, 30E20, 81T60, 44A60, 44A20, 33B15, 44A10, 45K05, 81Q40, 46N50 ACM classes: H.1.1 Cite as: arXiv:2604.07787 [quant-ph]   (or arXiv:2604.07787v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.07787 Focus to learn more Submission history From: Igor Kondrashuk [view email] [v1] Thu, 9 Apr 2026 04:29:19 UTC (91 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)