Allowed region and optimal measurement for information versus disturbance in quantum measurements

TL;DR

This paper analyzes the fundamental trade-offs between information gain and disturbance caused by quantum measurements, providing visualizations of allowed regions and identifying optimal measurement strategies.

Contribution

It introduces a comprehensive framework for quantifying information and disturbance in quantum measurements using multiple metrics and visualizes their trade-offs.

Findings

Allowed regions for information vs disturbance are mapped out.

Optimal measurements saturate bounds on information for given disturbance.

Framework broadens understanding of quantum measurement trade-offs.

Abstract

We present graphs of information versus disturbance for general quantum measurements of completely unknown states. Each piece of information and disturbance is quantified by two measures: (i) the Shannon entropy and estimation fidelity for the information and (ii) the operation fidelity and physical reversibility for the disturbance. These measures are calculated for a single outcome and are plotted on four types of information--disturbance planes to show their allowed regions. In addition, we discuss the graphs of these metrics averaged over all possible outcomes and the optimal measurements when saturating the upper bounds on the information for a given disturbance. The results considerably broaden the perspective of trade-offs between information and disturbances in quantum measurements.