A universally valid Heisenberg uncertainty relation

TL;DR

This paper introduces a new Heisenberg uncertainty relation that rigorously combines intrinsic quantum fluctuations with measurement effects, providing a universally valid formulation.

Contribution

It presents a mathematically rigorous uncertainty relation unifying error-disturbance and intrinsic quantum uncertainties, extending previous formulations.

Findings

Provides a universally valid uncertainty relation combining measurement and quantum fluctuations.

Mathematically rigorous formulation similar to Kennard and Robertson relations.

Incorporates both measurement effects and intrinsic quantum uncertainties.

Abstract

A universally valid Heisenberg uncertainty relation is proposed by combining the universally valid error-disturbance uncertainty relation of Ozawa with the relation of Robertson. This form of the uncertainty relation, which is defined with the same mathematical rigor as the relations of Kennard and Robertson, incorporates both of the intrinsic quantum fluctuations and measurement effects.