Quantifying Information Extraction using Generalized Quantum Measurements

TL;DR

This paper extends the concept of observational entropy to generalized quantum measurements, enabling analysis of indirect measurement schemes and their effectiveness in quantum information processing.

Contribution

It demonstrates that observational entropy's properties hold for generalized measurements, broadening its applicability beyond ideal projective measurements.

Findings

Observational entropy remains well-defined with generalized measurements.

Finite-dimensional probe limitations are analyzed.

Classical particle probes in von Neumann schemes are studied.

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 to provide adaptive measurement strategies alternative to quantum state tomography.