Abstract
Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the post-processing stage, it is inherent to first perceive the quantum state with a measurement protocol and store the information acquired. In this work, we propose a general framework for constructing classical approximations of arbitrary quantum states with quantum reservoirs. A key advantage of our method is that only a single local measurement setting is required for estimating arbitrary properties, while most of the previous methods need exponentially increasing number of measurement settings. To estimate properties simultaneously, the size of the classical approximation scales as . Moreover, this estimation scheme is extendable to higher-dimensional systems and hybrid systems with non-identical local dimensions, which makes it exceptionally generic. We support our theoretical findings with extensive numerical simulations.