Uncertainty relations for two observables coupled with the third one

TL;DR

This paper derives a new uncertainty relation for two observables entangled with a third, showing that the lower bound can be higher than traditional bounds, with implications for quantum state analysis.

Contribution

It introduces a novel lower boundary for the product of variances when two observables are entangled with a third, extending uncertainty principles.

Findings

New boundary can surpass Robertson--Schrödinger limit

Example provided with two-dimensional pure Gaussian states

Implications for quantum entanglement and measurement

Abstract

A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of the two-dimensional pure Gaussian state is considered as an example.