Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the postprocessing stage, it is inherent to first perceive the quantum state with a measurement protocol and store the information acquired. In this paper, 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 an exponentially increasing number of measurement settings. To estimate $M$ properties simultaneously, the size of the classical approximation scales as $lnM$. Moreover, this estimation scheme is extendable to higher-dimensional systems and hybrid systems with nonidentical local dimensions, which makes it exceptionally generic. We support our theoretical findings with extensive numerical simulations.

• Received 1 June 2023
• Accepted 23 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013211

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Published by the American Physical Society