Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators
Summarize this article with:
Quantum Physics arXiv:2601.01307 (quant-ph) [Submitted on 4 Jan 2026] Title:Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators Authors:Ayoub Ghaba, Radouan Hab Arrih, Elhoussine Atmani, Abdallah Slaoui View a PDF of the paper titled Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators, by Ayoub Ghaba and 3 other authors View PDF HTML (experimental) Abstract:Quantum steering is one of the most intriguing phenomena in quantum mechanics and is essential for understanding correlations in multi-body systems. Despite its importance, analytical results for coupled three-body oscillators remain scarce. In this work, we investigate this phenomenon through a geometrical diagonalization approach, which reduces the degrees of freedom associated with the system's steering properties. Specifically, we derive analytical expressions for quantum steering in all possible directions using the Wigner function framework, as it provides a complete description of the system's quantum state. Our results indicate that excitations significantly enhance quantum steering across the system; this stands in contrast to the ground state $(0,0,0)$, which exhibits no steerable correlations. Furthermore, both the directionality and topology of these correlations are governed by the spatial distribution of the excitations rather than their magnitude. We also observe symmetric steering behavior between oscillators $x$, $y$, and $z$ under equivalent excitation conditions, which can be formalized as $S^{(n,m,l)}_{x\to z}(\theta)=S^{(n,m,l)}_{x\to y}(-\theta),\quad S^{(n,m,l)}_{z\to x}(\theta)=S^{(n,m,l)}_{y\to x}(-\theta)$, and $S^{(n,m,l)}_{y\to z}(\theta)=S^{(n,m,l)}_{z\to y}(-\theta)$. Therefore, we elucidate how excitation levels and mixing angles generate and enhance steering in three coupled harmonic oscillators. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) Cite as: arXiv:2601.01307 [quant-ph] (or arXiv:2601.01307v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.01307 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Abdallah Slaoui [view email] [v1] Sun, 4 Jan 2026 00:08:14 UTC (3,580 KB) Full-text links: Access Paper: View a PDF of the paper titled Einstein-Podolsky-Rosen Steering in Three Coupled Harmonic Oscillators, by Ayoub Ghaba and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: math math-ph math.MP 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?)