Information-Theoretic Analysis of Weak Measurements and Their Reversal

TL;DR

This paper provides an information-theoretic analysis of null-result weak measurements in quantum systems, detailing how information is dynamically extracted and how measurement reversibility is characterized over time.

Contribution

It introduces a dynamical framework for quantifying information extraction in weak measurements for qubit, qutrit, and multilevel systems, emphasizing the evolution of information theoretic quantities.

Findings

Quantifies information extraction rate over time.

Analyzes the evolution of Shannon entropy, mutual information, fidelity, and relative entropy.

Highlights the dynamical nature of measurement reversibility.

Abstract

We study trade-off relations in information extraction from quantum systems subject to null-result weak measurements, where the absence of a detected photon continuously updates the system state. We present a detailed analysis of qubit and qutrit systems and investigate a general framework for a multilevel quantum system. We develop a dynamical characterization of null-result weak measurements that quantifies the information extracted over time, revealing the amount of the obtained information and also the rate of the information accumulation. The characterizations are obtained by examining the time-dependent evolution of the information theoretic quantities. More specifically, we consider Shannon entropy, mutual information, fidelity, and relative entropy to characterize the weak measurement dynamics. Our results provide an information theoretic analysis of the weak measurement process and highlight the dynamical nature of information extraction and reversibility in the weak measurement processes.