Measuring polynomial invariants of multiparty quantum states

The networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations were analyzed. It was shown that the networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). It was found the networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. The statistical efficiency of networks compared to methods based on estimating the state coefficients and calculating the invariants was described.