Talk:Mutually unbiased bases

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This article was created as a project for an Advanced Quantum Theory class. Edits, updates, fixed, etc are most certainly welcome. Mschirm (talk) 05:17, 14 November 2008 (UTC)[reply]

Claims about priority for mutually unbiased bases

The article attributes the first introduction of Mutually unbiased bases to Schwinger in 1960. I am not sure this is correctly stated, in few of the fact that the discrete fourier basis (for the discrete fourier transform) is a mutually unbiased basis. 60.250.123.226 (talk) 05:59, 13 October 2022 (UTC)[reply]

The phrase used is, "The notion of mutually unbiased bases was first introduced by Schwinger in 1960," which, in my reading, is saying that he identified a set of desirable properties ("optimum degree of incompatibility") and made a definition ("complementary pair of operators"). (See page 575 of Schwinger's paper, especially footnote 3, for which you will have to turn to the end of the article.) Assuming he was the first to do so, I would say the phrasing is okay. It's not terribly surprising that sets of operators having those desirable properties would already have been known. The question is whether the properties and their significance were recognized earlier.

If you can suggest a good authoritative source on the history that sheds light on this, perhaps we can have a look at that to determine whether the attribution needs to be altered. Will Orrick (talk) 12:25, 14 October 2022 (UTC)[reply]