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This tutorial aims to provide a basic introduction to Haar measure tools in quantum information, utilizing only basic knowledge of linear algebra and thus aiming to make this topic more accessible. The tutorial begins by introducing the Haar measure with a specific emphasis on characterizing the moment operator, an essential element for computing integrals over the Haar measure. It also covers properties of the symmetric subspace and introduces helpful tools like tensor network diagrammatic notation, which aid in visualizing and simplifying calculations. Next, the tutorial explores the concept of unitary designs, providing equivalent definitions, and subsequently explores approximate notions of unitary designs, shedding light on the relationships between these different notions. Practical examples of Haar measure calculations are illustrated, including the derivation of well-known formulas such as the twirling of a quantum channel. Lastly, the tutorial showcases the applications of Haar measure calculations in quantum machine learning and classical shadow tomography.<\/jats:p>","DOI":"10.22331\/q-2024-05-08-1340","type":"journal-article","created":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T09:37:56Z","timestamp":1715161076000},"page":"1340","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":114,"title":["Introduction to Haar Measure Tools in Quantum Information: A Beginner&apos;s Tutorial"],"prefix":"10.22331","volume":"8","author":[{"given":"Antonio Anna","family":"Mele","sequence":"first","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2024,5,8]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Hsin-Yuan Huang, Richard Kueng, and John Preskill, ``Predicting many properties of a quantum system from very few measurements'' Nature Physics 16, 1050-1057 (2020).","DOI":"10.1038\/s41567-020-0932-7"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Jeongwan Haah, Aram W. 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