We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our 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. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.
|Translated title of the contribution||Measuring polynomial invariants of multiparty quantum states|
|Article number||Art. No. 052304|
|Journal||Physical Review A: Atomic, Molecular and Optical Physics|
|Publication status||Published - May 2004|
Bibliographical notePublisher: American Physical Soc
Other identifier: IDS Number: 826FC