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We propose an ordered set of experimentally accessible conditions fordetecting entanglement in mixed states. The $k$-th condition involves comparingmoments of the partially transposed density operator up to order $k$.Remarkably, the union of all moment inequalities reproduces the Peres-Horodeckicriterion for detecting entanglement. Our empirical studies highlight that thefirst four conditions already detect mixed state entanglement reliably in avariety of quantum architectures. Exploiting symmetries can help to furtherimprove their detection capabilities. We also show how to estimate momentinequalities based on local random measurements of single state copies(classical shadows) and derive statistically sound confidence intervals as afunction of the number of performed measurements. Our analysis includes theexperimentally relevant situation of drifting sources, i.e. non-identical, butindependent, state copies.

Symmetry-resolved entanglement detection using partial transpose moments