Probability representation and state-extended uncertainty relations

TL;DR

This paper explores the state-extended uncertainty relations within the tomographic-probability framework of quantum mechanics, enabling experimental verification through optical homodyne detection of photon states.

Contribution

It reformulates Trifonov's state-extended inequality using optical tomograms, bridging theoretical uncertainty relations with practical experimental methods.

Findings

Expressed Trifonov inequalities in terms of optical tomograms

Proposed experimental verification via homodyne detection

Enhanced understanding of quantum state uncertainties

Abstract

The new inequality recently found by Trifonov and called the state-extended inequality is considered in the tomographic-probability representation of quantum mechanics. The Trifonov uncertainty relations are expressed in terms of optical tomograms and can be checked in experiments on homodyne detection of the photon states.