Permutation Invariant Optimization Problems in Quantum Information Theory: A Framework for Channel Fidelity and Beyond
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Quantum Physics arXiv:2604.27040 (quant-ph) [Submitted on 29 Apr 2026] Title:Permutation Invariant Optimization Problems in Quantum Information Theory: A Framework for Channel Fidelity and Beyond Authors:Bjarne Bergh, Marco Parentin View a PDF of the paper titled Permutation Invariant Optimization Problems in Quantum Information Theory: A Framework for Channel Fidelity and Beyond, by Bjarne Bergh and 1 other authors View PDF HTML (experimental) Abstract:Exploiting permutation invariance to reduce the exponential scaling of semidefinite programs in quantum information has emerged as a powerful computational technique. In this work, we develop a systematic framework for using this reduction via Schur-Weyl duality for optimization problems, and establish methods that allow one to work fully inside the permutation invariant subspace while performing operations such as (partially) applying channels and taking (partial) traces, or computing expressions like the quantum relative entropy. We then apply our techniques to the problem of computing efficient lower bounds on the channel fidelity over $n$ parallel uses of a quantum channel. The algorithm, which we call symmetric seesaw method, exploits permutation-invariant codes to yield improved lower bounds on the channel fidelity over $n$ uses of the depolarizing and amplitude-damping channel in the regime of tens of channel uses, and was used in [Parentin, Bergh, Datta, Wilde: Onset of superactivation of quantum capacity, arXiv: today] to demonstrate non-asymptotic superactivation of quantum capacity for $n = 17$. An implementation of our methods, aimed at being suitable for various quantum information theoretic optimization problems, is also available as an open-source Python package. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.27040 [quant-ph] (or arXiv:2604.27040v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.27040 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bjarne Bergh [view email] [v1] Wed, 29 Apr 2026 17:14:00 UTC (589 KB) Full-text links: Access Paper: View a PDF of the paper titled Permutation Invariant Optimization Problems in Quantum Information Theory: A Framework for Channel Fidelity and Beyond, by Bjarne Bergh and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)