Uncertainty Relation Revisited from Quantum Estimation Theory

TL;DR

This paper revisits the quantum uncertainty principle by applying quantum estimation theory to derive bounds on measurement errors for arbitrary quantum states and observables, confirming and refining Heisenberg's relation.

Contribution

It introduces a quantum estimation theory framework to formulate and attain bounds on measurement errors, providing a new perspective on the uncertainty principle.

Findings

Heisenberg's uncertainty relation is satisfied for arbitrary states and observables.

The paper derives the attainable bound of measurement errors.

A strategy to achieve the bound is proposed.

Abstract

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy Heisenberg's uncertainty relation, find the attainable bound, and provide a strategy to achieve it.