Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions
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Quantum Physics arXiv:2605.02986 (quant-ph) [Submitted on 4 May 2026] Title:Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions Authors:Ammar Daskin View a PDF of the paper titled Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions, by Ammar Daskin View PDF Abstract:The linear combination of unitaries (LCU) is a fundamental quantum algorithm primitive that embeds non-unitary operators via post-selection on an ancilla register. In standard LCU, only the $|0\dots0\rangle$ ancilla outcome is retained; the remaining "junk" outcomes are discarded. We study these discarded parts by introducing an alternative LCU circuit which simplifies the coefficient preparation unitary with Hadamard gates and a single rotation qubit. Every computational basis measurement of the ancilla projects the system onto a different linear combination of the target unitaries. Collecting these outcome states and reshaping them into a $2K\times N$ matrix reveals a factorization $\Phi = C X$, where $C$ encodes the coefficients and $X$ contains the action of each unitary on the input; this immediately shows $\operatorname{rank}(\Phi)\le K$. This structure enables two complementary applications: (i) classical low-rank matrix completion can reconstruct the full output (including the target) from a fraction of its entries, turning every shot into useful information; (ii) treating $C$ as a secret key hides the input state, leading to a candidate quantum trapdoor function and symmetric encryption. The scheme thus turns the "junk" ancilla outcomes into a structured resource, possibly opening paths for further applications. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.02986 [quant-ph] (or arXiv:2605.02986v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.02986 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ammar Daskin [view email] [v1] Mon, 4 May 2026 12:05:47 UTC (67 KB) Full-text links: Access Paper: View a PDF of the paper titled Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions, by Ammar DaskinView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)