  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 $M$ properties
simultaneously, the size of the classical approximation scales as $\ln M$ .
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.
