Absolute Schmidt number: characterization, detection and resource-theoretic quantification

Quantum Physics [Submitted on 2 Apr 2026] Absolute Schmidt number: characterization, detection and resource-theoretic quantification Bivas Mallick, Saheli Mukherjee, Nirman Ganguly, A. S. Majumdar The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states whose Schmidt number cannot be increased by any global unitary transformation. We provide a characterization of the set of arbitrary-dimensional states whose Schmidt number is invariant under all global unitaries. Our approach enables us to develop both witness-based and moment-based techniques to detect nonabsolute Schmidt number states which could provide significant operational advantages through Schmidt number enhancement by global unitaries. We next formulate two resource-theoretic measures of nonabsolute Schmidt number states, based respectively on Schmidt number witness and robustness, and demonstrate an operational utility of the latter in a channel discrimination task. Finally, we extend our analysis to quantum channels by introducing a new class of channels that possess the absolute Schmidt number property. We derive a necessary and sufficient condition for identifying when a channel has the absolute Schmidt number property, confining our analysis to the class of covariant channels. Comments: 25 pages, Comments are welcome Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02439 [quant-ph]   (or arXiv:2604.02439v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.02439 Focus to learn more Submission history From: Bivas Mallick [view email] [v1] Thu, 2 Apr 2026 18:10:13 UTC (36 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?)