Operator theory in quantum information processing

Kulkarni, Chaitanya S.; Kwatra, Heena; Dhawas, Nitin; Gandal, Ganesh; Sabirov, Sardor; Londhe, Gayatri Dattatraya; Isaev, Fakhriddin

doi:10.47974/JIM-2510

Open Access Research Article

Operator theory in quantum information processing

Chaitanya S. Kulkarnichaitanya.kulkarni2886@gmail.comDepartment of Artificial Intelligence and Data Science Vidya Pratishthan’s Kamalnayan Bajaj Institute of Engineering & TechnologyBaramati, Maharashtra, 413133, IndiaView full profile → , ^*Heena KwatraCorresponding authorhnkwatra1989@gmail.comDepartment of Computer Science and Engineering Bharati Vidyapeeth’s College of EngineeringNew Delhi, Delhi, 110063, IndiaView full profile → , Nitin Dhawasnitin.dhawas@nmiet.edu.inDepartment of Electronics & Telecommunication Engineering Nutan Maharashtra Institute of Engineering & TechnologyDepartment of Electronics and Telecommunication Engineering Nutan Maharashtra Institute of Engineering and TechnologyPune, Maharashtra, 410507, IndiaView full profile → , Ganesh Gandalganesh.gandal_skncoe@sinhgad.eduDepartment of Mathematics Smt. Kashibai Navale College of EngineeringPune, Maharashtra, 411041, IndiaView full profile → , Sardor Sabirovsabirov_sardor@mamunedu.uzDepartment of General Professional Sciences Mamun UniversityKhiva, 220900, UzbekistanView full profile → , Gayatri Dattatraya Londhegayatri.londhe@dypvp.edu.inDepartment of Electronics & Telecommunication Dr. D. Y. Patil Institute of Technology PimpriDepartment of Electronics & Telecommunication Dr. D. Y. Patil Institute of Technology PimpriPune, Maharashtra, 411018, IndiaView full profile → , Fakhriddin Isaevfakhriddin.isaev@tues.uz; f.isaev@tsue.uzDepartment of Finance and Tourism Termez University of Economics and Service; Center for Economic Development Research (CEDR) Tashkent State University of EconomicsDepartment of Finance and Tourism Termez University of Economics and ServiceTermez, 190111, UzbekistanView full profile →

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pp. 739–747Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2510XML

Received:: 01 Mar 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2510
Pages:: 739–747

Abstract

This paper looks at how operator theory can be used as a strict mathematical framework for processing quantum information. It discusses about how Hilbert spaces, spectral theory, and operator algebras can be used to describe quantum systems. The study also looks at Kraus decomposition and Stinespring dilation to talk about quantum channels and how they can be interpreted physically. In this study operator-theoretic method provide the huge data related to entanglement, decoherence, and channel stability by integrating the method as functional analysis with quantum physics.

Keywords

Operator theory Quantum channels Kraus decomposition Stinespring dilation Quantum inform-ation processing

Subject Classifications

54H3068Q09

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