Quantum Framework for Wavelet Shrinkage

Quantum Physics arXiv:2511.19855 (quant-ph) [Submitted on 25 Nov 2025] Title:Quantum Framework for Wavelet Shrinkage Authors:Brani Vidakovic View a PDF of the paper titled Quantum Framework for Wavelet Shrinkage, by Brani Vidakovic View PDF HTML (experimental) Abstract:This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients is carried out through controlled decoherence rather than nonlinear thresholding. Phase damping and ancilla-driven constructions realize this behavior coherently and show that statistical adaptivity and quantum unitarity can be combined within a single circuit model. The same physical mechanisms that reduce quantum coherence, such as dephasing and amplitude damping, are repurposed as programmable resources for noise suppression. Practical demonstrations implemented with Qiskit illustrate how circuits and channels emulate coefficientwise attenuation, and all examples are provided as Jupyter notebooks in the companion GitHub repository. Encoding schemes for amplitude, phase, and hybrid representations are examined in relation to transform coherence and measurement feasibility, and realizations suited to current noisy intermediate-scale quantum devices are discussed. The work provides a conceptual and experimental link between wavelet-based statistical inference and quantum information processing, and shows how engineered decoherence can act as an operational surrogate for classical shrinkage. Comments: Subjects: Quantum Physics (quant-ph); Computation (stat.CO) Cite as: arXiv:2511.19855 [quant-ph] (or arXiv:2511.19855v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.19855 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Brani Vidakovic [view email] [v1] Tue, 25 Nov 2025 02:35:18 UTC (1,678 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Framework for Wavelet Shrinkage, by Brani VidakovicView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: stat stat.CO References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)