The Pareto Frontiers of Magic and Entanglement: The Case of Two Qubits

Quantum Physics [Submitted on 26 Mar 2026] The Pareto Frontiers of Magic and Entanglement: The Case of Two Qubits Alexander Roman, Marco Knipfer, Jogi Suda Neto, Konstantin T. Matchev, Katia Matcheva, Sergei Gleyzer Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, M_2, and entanglement by the concurrence \Delta. We find that the Pareto frontier of maximal magic M_2^{(max)}(\Delta) is composed of three separate segments, while the boundary of minimal magic M_2^{(min)}(\Delta) is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement. Comments: 34 pages, 8 figures Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET); High Energy Physics - Lattice (hep-lat); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2603.24902 [quant-ph]   (or arXiv:2603.24902v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.24902 Focus to learn more Submission history From: Konstantin Matchev [view email] [v1] Thu, 26 Mar 2026 00:32:43 UTC (939 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.ET hep-lat hep-ph hep-th 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?)