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In this work, we investigate efficient estimation strategies of these observables based on a joint measurement which, after classical post-processing, yields all sufficiently unsharp (noisy) Majorana observables of even-degree. By exploiting the symmetry properties of the Majorana observables, as described by the braid group, we show that the incompatibility robustness, i.e., the minimal classical noise necessary for joint measurability, relates to the spectral properties of the Sachdev-Ye-Kitaev (SYK) model. In particular, we show that for an\n \n n<\/mml:mi>\n <\/mml:math>\n mode fermionic system, the incompatibility robustness of all degree-\n \n 2<\/mml:mn>\n k<\/mml:mi>\n <\/mml:math>\n Majorana observables satisfies\n \n &#x0398;<\/mml:mi>\n (<\/mml:mo>\n \n n<\/mml:mi>\n \n &#x2212;<\/mml:mo>\n k<\/mml:mi>\n \n \/<\/mml:mo>\n <\/mml:mrow>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:math>\n for\n \n k<\/mml:mi>\n &#x2264;<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:math>\n . Furthermore, we present a joint measurement scheme achieving the asymptotically optimal noise, implemented by a small number of fermionic Gaussian unitaries and sampling from the set of all Majorana monomials. Our joint measurement, which can be performed via a randomization over projective measurements, provides rigorous performance guarantees for estimating fermionic observables comparable with fermionic classical shadows.\n <\/jats:p>","DOI":"10.22331\/q-2025-11-17-1914","type":"journal-article","created":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T16:43:09Z","timestamp":1763397789000},"page":"1914","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3276-0587","authenticated-orcid":false,"given":"Daniel","family":"McNulty","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Bari, 70126 Bari, Italy"},{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnik\u00f3w 32\/46, 02-668 Warszawa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Susane","family":"Calegari","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnik\u00f3w 32\/46, 02-668 Warszawa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4946-6835","authenticated-orcid":false,"given":"Micha\u0142","family":"Oszmaniec","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnik\u00f3w 32\/46, 02-668 Warszawa, Poland"},{"name":"NASK National Research Institute, ul. 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