Simultaneous measurability of error and disturbance

TL;DR

This paper investigates the simultaneous measurability of error and disturbance in quantum measurements, proposing a new inequality and providing a testable example to deepen understanding of quantum uncertainty relations.

Contribution

It introduces a novel inequality involving error and disturbance measured in the same quantum state, addressing a gap in the understanding of their simultaneous measurability.

Findings

Proposes a new inequality for error and disturbance in the same state

Suggests a testable example demonstrating the inequality

Enhances understanding of quantum measurement uncertainty

Abstract

The uncertainty relation, which displays an elementary property of quantum theory, was originally described by Heisenberg as the relation between error and disturbance. Ozawa presented a more rigorous expression of the uncertainty relation, which was later verified experimentally. Nevertheless, the operators corresponding to error and disturbance should be measurable in the identical state if we follow the presupposition of Heisenberg's thought experiment. In this letter, we discuss simultaneous measurability of error and disturbance and present a new inequality using error and disturbance in the identical state. A testable example of this inequality is also suggested.