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Peer-reviewedCC BY 4.0Mathematics

Inverse Laplace and Mellin Integral Transforms Modified for Use in Quantum Communications

  • Gustavo Álvarez1
  • Igor Kondrashuk2,3,4
4 affiliations
  1. 1II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
  2. 2Grupo de Matemática Aplicada, Departamento de Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Av. Andres Bello 720, Casilla 447, Chillán 3780227, Chile
  3. 3Grupo de Física de Altas Energías, Departamento de Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Av. Andres Bello 720, Casilla 447, Chillán 3780227, Chile
  4. 4Centro de Ciencias Exactas, Departamento de Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Av. Andres Bello 720, Casilla 447, Chillán 3780227, Chile
Open at sourceDOICite

Abstract

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—particularly 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 the 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 present a brief review of the basic integral transforms and propose their modification for the extended domains.

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Cite

BibTeXRIS
BibTeX
@article{alvarez2026inverse,
  title = {{Inverse Laplace and Mellin Integral Transforms Modified for Use in Quantum Communications}},
  author = {Gustavo Álvarez and Igor Kondrashuk},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203820},
  url = {https://www.mdpi.com/2227-7390/14/20/3820},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Inverse Laplace and Mellin Integral Transforms Modified for Use in Quantum Communications
AU  - Gustavo Álvarez
AU  - Igor Kondrashuk
PY  - 2026
DA  - 2026/10/20
JO  - Mathematics
DO  - 10.3390/math14203820
UR  - https://www.mdpi.com/2227-7390/14/20/3820
AB  - 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—particularly 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 the 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 present a brief review of the basic integral transforms and propose their modification for the extended domains.
SN  - 2227-7390
ER  -