Classical shadow protocols using uniform sampling over compact symmetric spaces admit a unifying theory and yield slight sample-complexity improvements over standard schemes for certain observable distributions.
Duenez, Random matrix ensembles associated to com- pact symmetric spaces, Communications in mathematical physics244, 29 (2004)
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Classical shadows over symmetric spaces
Classical shadow protocols using uniform sampling over compact symmetric spaces admit a unifying theory and yield slight sample-complexity improvements over standard schemes for certain observable distributions.