Robertson-Schr\"odinger formulation of Ozawa's Uncertainty Principle

TL;DR

This paper introduces a Robertson-Schr"odinger formulation of the measurement disturbance uncertainty principle, which is stronger, invariant under symplectic transformations, and can be saturated by certain probe states.

Contribution

It presents a more general and robust formulation of the measurement disturbance uncertainty principle, improving upon Ozawa's relations with better mathematical properties.

Findings

The new formulation is stronger than Ozawa's uncertainty relations.

It is invariant under symplectic transformations.

Certain probe states can saturate the matrix formulation.

Abstract

A more general measurement disturbance uncertainty principle is presented in a Robertson-Schr\"odinger formulation. It is shown that it is stronger and having nicer properties than Ozawa's uncertainty relations. In particular is invariant under symplectic transformations. One shows also that there are states of the probe (measuring device) that saturate the matrix formulation of measurement disturbance uncertainty principle.