An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles

Quantum Physics arXiv:2607.01564 (quant-ph) [Submitted on 2 Jul 2026] Title:An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles Authors:Farhad Farokhi, Shuixin Xiao View a PDF of the paper titled An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles, by Farhad Farokhi and 1 other authors View PDF HTML (experimental) Abstract:Optimal encoding of classical data for quantum-assisted statistical inference is investigated from an information-theoretic perspective. We prove that the accuracy of any quantum-computing inference procedure is upper bounded by the maximal quantum leakage from the classical data through its quantum encoding, establishing leakage as a universal, task-agnostic quality measure for encoders. This demonstrates that the maximal quantum leakage is a universal measure of the quality of the encoding strategy for statistical inference as it only depends on the quantum encoding of the data and not the inference task itself. The optimal universal encoding strategy, i.e., an encoding strategy that maximizes the maximal quantum leakage, is proved to be attained by pure states. When there are enough qubits, basis encoding is proved to be universally optimal. However, when the dimension of the system is small, phase encoding is optimal. For the latter, any tight frame, any ensemble whose average state is the maximally mixed state, is in fact optimal. Within tight frames, equiangular tight frames (ETFs) are distinguished as the uniquely symmetric optimal encodings, i.e., they saturate the Welch lower bound on pairwise overlaps and possess a self-referential optimal measurement. Prominent special cases are the qubit trine, the regular simplex, and symmetric informationally complete positive operator-valued measures (SIC-POVMs), for which the ETF structure and explicit codeword constructions are provided. Numerical examples are presented to validate the theoretical predictions. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2607.01564 [quant-ph] (or arXiv:2607.01564v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.01564 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Farhad Farokhi [view email] [v1] Thu, 2 Jul 2026 00:45:51 UTC (155 KB) Full-text links: Access Paper: View a PDF of the paper titled An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles, by Farhad Farokhi and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: cs cs.IT math math.IT 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?) 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?)