How can we check the uncertainty relation?

TL;DR

This paper presents a method for experimentally verifying generalized uncertainty relations using homodyne detection and discusses analyzing entanglement through qubit portraits of qudit states via tomographic probabilities.

Contribution

It introduces a form of state-extended uncertainty relations suitable for experimental testing and explores a novel approach to analyze entanglement using qubit portraits of qudit states.

Findings

Derived uncertainty relations suitable for homodyne detection

Proposed a method to analyze entanglement via qubit portraits

Discussed experimental implementation of the uncertainty check

Abstract

The state-extended uncertainty relations generalizing the Robertson Schrodinger inequality are presented in the form appropriate for the experimental check by homodyne photon state detection. The method of qubit portrait of qudit states identified with the tomographic probability distributions is discussed to analyze the entanglement of two-mode field.