Coherence and entanglement dynamics in Shor's algorithm

Quantum Physics [Submitted on 8 Apr 2026] Coherence and entanglement dynamics in Shor's algorithm Linlin Ye, Zhaoqi Wu, Shao-Ming Fei Shor's algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm, showing that the coherence in each step relies on the dimension of register or the order, and discuss the relations between geometric coherence and geometric entanglement. We investigate how unitary operators induce variations in coherence and entanglement, and analyze the variations of coherence and entanglement within the entire algorithm, demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement. Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms. Comments: 19 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.06639 [quant-ph]   (or arXiv:2604.06639v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.06639 Focus to learn more Journal reference: Commun. Theor. Phys. 78 (2026) 015102 Related DOI: https://doi.org/10.1088/1572-9494/adf8cc Focus to learn more Submission history From: Zhaoqi Wu [view email] [v1] Wed, 8 Apr 2026 03:25:43 UTC (147 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?)