From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states

Quantum Physics [Submitted on 3 Apr 2026] From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states Zhu-yao Jin, J. Q. You, Jun Jing 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: 5+17 pages, 2 figures 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 Submission history From: Jun Jing [view email] [v1] Fri, 3 Apr 2026 02:01:49 UTC (502 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)