Tradeoff Relation between Information and Disturbance in Quantum Measurement

TL;DR

This paper establishes a quantitative tradeoff relation between information gain and disturbance in quantum measurements using an estimation-theoretic framework, highlighting conditions for equality and extending to various divergences.

Contribution

It formulates a new inequality linking classical Fisher information and quantum Fisher information loss, providing a unified perspective on measurement disturbance in quantum systems.

Findings

Pure and reversible measurements achieve equality in the tradeoff relation.

The relation holds for quantum relative entropy and its maximum variant.

Necessary conditions are identified for divergence-based relations.

Abstract

When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff relations between information and disturbance. We formulate a tradeoff relation between information and disturbance from an estimation-theoretic point of view, and derive an inequality between them. The information is defined as the classical Fisher information obtained by the measurement, and the disturbance is defined as the average loss of the quantum Fisher information. We show that pure and reversible measurements achieve the equality of the inequality. We also identify the necessary condition for various divergences between two quantum states to satisfy a similar relation. The obtained relation holds not only for the quantum relative entropy but also for the maximum quantum relative entropy.