Perfect $(s,r)$-state transfer

Quantum Physics arXiv:2609.10713 (quant-ph) [Submitted on 9 Sep 2026] Title:Perfect $(s,r)$-state transfer Authors:Stephen Kirkland, Hermie Monterde, Sarah Plosker View a PDF of the paper titled Perfect $(s,r)$-state transfer, by Stephen Kirkland and 2 other authors View PDF HTML (experimental) Abstract:Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirected graph, and studying vertex-to-vertex dynamics. This setup has recently been relaxed to allow for dynamics between linear combinations of two vertex states, i.e.\ from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf \mu=\mathbf e_{\alpha} + r \mathbf e_{\beta}$, where $r=s$ is either $-1$ (which corresponds to pair state transfer) or $+1$ (which corresponds to plus state transfer), or more recently $r=s$ is taken to be any real number (which corresponds to $s$-pair state transfer). Here, we broaden the investigation of $s$-pair state transfer to \textit{perfect $(s,r)$-state transfer}, which is perfect state transfer from $\mathbf u = \mathbf e_a + s \mathbf e_b$ to $\mathbf \mu=\mathbf e_{\alpha} + r \mathbf e_{\beta}$ (up to some dilation) where $r,s\in \mathbb C$. We identify infinite families of graphs with perfect $(s,r)$-state transfer and provide characterizations of cases when $|r|= |s|$ and when $|r|\neq |s|$, showing situations when the degree of entanglement between vertex states is preserved, and when it is not preserved. The latter is particularly important as it represents perfect state transfer from an entangled pair of qubits to another one where the degree of entanglement need not be the same\mdash in fact, it can be set up so as to ``boost'' (increase) entanglement. We provide an algorithm that finds the vector with two nonzero entries that maximizes the fidelity of transfer for a fixed time $t$ starting from a given $s$-pair state $\mathbf u$. Finally, we provide a sensitivity analysis, with respect to readout time errors, of perfect $(s,r)$-state transfer. Comments: Subjects: Quantum Physics (quant-ph); Combinatorics (math.CO) MSC classes: 05C50, 81P45, 05C76, 15A18, 81Q10 Report number: PIMS-20260909-PDF Cite as: arXiv:2609.10713 [quant-ph] (or arXiv:2609.10713v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.10713 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sarah Plosker [view email] [v1] Wed, 9 Sep 2026 18:10:33 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Perfect $(s,r)$-state transfer, by Stephen Kirkland and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: math math.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?) 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?)