Derivative of the disturbance with respect to information from quantum measurements

TL;DR

This paper analyzes how disturbance in quantum measurements changes with information, using derivatives to understand the boundaries of feasible measurement regions in quantum information theory.

Contribution

It derives the first and second derivatives of disturbance relative to information for key quantum measurements, clarifying the shape of the allowed regions in information-disturbance space.

Findings

Identifies the slopes and curvatures of boundary regions in quantum measurement spaces.

Provides a mathematical framework for analyzing trade-offs in quantum information.

Clarifies the geometric structure of feasible measurement regions.

Abstract

To study the trade-off between information and disturbance, we obtain the first and second derivatives of the disturbance with respect to information for a fundamental class of quantum measurements. We focus on measurements lying on the boundaries of the physically allowed regions in four information--disturbance planes, using the derivatives to investigate the slopes and curvatures of these boundaries and hence clarify the shapes of the allowed regions.