Quantifying information extraction using generalized quantum measurements

Abstract

Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show that the same properties hold even when considering generalized measurements. Thus, the interpretation still holds: Observational entropy is a well-defined quantifier determining how influential a given series of measurements is in information extraction. This generalized framework allows for the study of the performance of indirect measurement schemes, which are those using a probe. Using this framework, we first analyze the limitations of a finite-dimensional probe. Then we study several scenarios of the von Neumann measurement scheme, in which the probe is a classical particle characterized by its position. Finally, we discuss observational entropy as a tool for quantum-state inference. Further developed, this framework could find applications in quantum information processing. For example, it could help in determining the best read-out procedures from quantum memories and providing adaptive measurement strategies alternative to quantum-state tomography. © 2023 American Physical Society.