Entanglement and Quantum Coherence in Krylov Space Dynamics

Quantum Physics [Submitted on 27 Mar 2026] Entanglement and Quantum Coherence in Krylov Space Dynamics Swati Choudhary, Sukrut Mondkar, Ujjwal Sen The spreading of quantum states in Krylov space under unitary dynamics provides a natural framework for characterizing quantum complexity. Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio, depend explicitly on both the Hamiltonian and the initial state, rendering their connection to fundamental quantum resources such as entanglement and quantum coherence subtle. We establish quantitative bounds relating Krylov-space spreading to the entanglement of the evolved state and to the quantum coherence of the initial state. For bipartite systems, we have shown that the entanglement of the evolved state is upper bounded in terms of the entanglement of the Krylov basis vectors and the spread complexity. In the case of multipartite systems, analogous bounds are obtained for the inverse participation ratio, a quantifier of the delocalization of a quantum state in the Krylov basis, in terms of the geometric measures. Furthermore, for qubit and qutrit systems, we derive relations between the quantum coherence of the initial state in the energy eigenbasis and the spread complexity, valid for arbitrary Hamiltonians. Our results provide quantitative constraints linking Krylov-space complexity growth to fundamental quantum resources. Comments: 10 pages Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.26619 [quant-ph]   (or arXiv:2603.26619v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.26619 Focus to learn more Submission history From: Swati Choudhary [view email] [v1] Fri, 27 Mar 2026 17:15:24 UTC (26 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 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?)