STATE-EXTENDED UNCERTAINTY RELATIONS AND TOMOGRAPHIC INEQUALITIES AS QUANTUM SYSTEM STATE CHARACTERISTICS
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 uncertainty relation are considered. Tomographic cumulant related to photon state tomographic probability distributions is introduced and it is used as parameter of the state non-Gaussianity.
uncertainty relations probability vector cumulant quantum tomograms non-gaussianity parameter semigroup