Efficient preparation of ensemble moment states

Determine whether the moment states \(\rho^{(k)}_{\mathcal E}\) of projected quantum-state ensembles can be prepared directly and efficiently without sampling individual projected states.

Background

The projected ensemble is naturally described through its statistical moment states, which encode the ensemble’s higher-order fluctuations. Directly reconstructing the underlying projected states is experimentally expensive because repeated observations of the same bath outcome are required.

The paper raises direct preparation of the moment states as an alternative experimental and theoretical route to studying quantum statistical mechanics, but leaves open whether this can be achieved efficiently.