State-extended uncertainly relations and tomographic inequalities as quantum system state characteristics

TL;DR

This paper explores inequalities for quantum state tomograms, introduces a tomographic cumulant for photon states, and discusses an extended uncertainty relation within the probability representation of quantum mechanics.

Contribution

It presents new inequalities for quantum tomograms and introduces a tomographic cumulant as a measure of non-Gaussianity, extending the understanding of quantum state characteristics.

Findings

Derived inequalities for qudit tomograms

Introduced a tomographic cumulant for photon states

Proposed an extended uncertainty relation

Abstract

Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used. Examples of inequalities for qudit tomograms and a state extended uncertainly relation are considered. Tomographic cumulant related to photon state tomographic probability distributions is introduced and it is used as parameter of the state nongaussianity.