Balance between information gain and reversibility in weak measurement

TL;DR

This paper establishes a precise quantitative relationship between the information gained from weak quantum measurements and the probability of reversing those measurements, enhancing understanding of measurement reversibility in quantum systems.

Contribution

It derives a tight bound linking measurement quality and reversibility, providing a comprehensive framework for analyzing weak measurements in arbitrary-dimensional quantum systems.

Findings

Derived a tight bound between information gain and reversibility.

Showed that information from weak measurements can be erased through reversal.

Provided a new standard for characterizing weak measurements and reversals.

Abstract

We derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the information gain and reversibility. In this formulation, it is clearly shown that the information extracted from a weak measurement is erased through the reversing process. Our result broadens the information-theoretic perspective on quantum measurement as well as provides a standard tool to characterize weak measurements and reversals.