From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states
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Quantum Physics arXiv:2604.02635 (quant-ph) [Submitted on 3 Apr 2026] Title:From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states Authors:Zhu-yao Jin, J. Q. You, Jun Jing View a PDF of the paper titled From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states, by Zhu-yao Jin and 2 other authors View PDF HTML (experimental) Abstract:Within a unified framework, we reveal that the seemingly disparate control approaches for classical and quantum continuous-variable systems are interconnected via differential manifolds of the ancillary representations. For classical systems, the ancillary representation is defined by the time-dependent ancillary canonical variables resulting from a symplectic transformation over the original canonical variables. Under the conditions of the Hamilton-Jacobi equation, the ancillary canonical variables act as dynamical invariants to guide the system nonadiabatically through the entire phase space. The second quantization of the Liouville equation for the canonical variables leads to the Heisenberg equation for the relevant ancillary operators, which is found to be a sufficient condition to yield nonadiabatic passages towards arbitrary target states in both Hermitian and non-Hermitian systems and constrained exact solutions of the time-dependent Schroedinger equation. Using the non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation, our theory is exemplified by the generation of single-mode squeezed states with a squeezing level of 29.3 dB and double-mode squeezed states with 20.5 dB, respectively. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02635 [quant-ph] (or arXiv:2604.02635v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.02635 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jun Jing [view email] [v1] Fri, 3 Apr 2026 02:01:49 UTC (502 KB) Full-text links: Access Paper: View a PDF of the paper titled From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states, by Zhu-yao Jin and 2 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?)