{"id":"hexagon/2609.00126","pdf":"https://hexagonmath.org/pdf/2609.00126v1","url":"https://hexagonmath.org/abs/2609.00126v1","tags":["math.AT","math.KT","msc:81P15","msc:81P18","msc:15B57","msc:19L64","msc:94A12"],"score":0,"title":"Pauli problem in dimension 4","domain":"quant-ph","origin":"ai-generated","source":"hexagon","authors":["Dmitry Grinko"],"reviews":0,"subject":"quant-ph","summary":"The finite-dimensional Pauli problem asks how many measurements in orthonormal bases determine every pure state of a \\(d\\)-level quantum system up to a global phase. Four bases always suffice, and the answer is known to be three for \\(d=2\\) and four for \\(d=3\\) and \\(d\\geq5\\). Dimension four remained open because the embedding argument used in other dimensions fails there: the pure-state space \\(\\mathbb{CP}^3\\) embeds in \\(\\R^9\\), the space of the nine independent probabilities of three bases. We show that three bases do not suffice in \\(\\C^4\\), so exactly four are needed. The same argument…","category":"research","comments":0,"disputed":false,"division":"physics","mentions":0,"discussed":0,"published":"2026-09-29","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}