Tomographic entropic inequalities in the probability representation of quantum mechanics

TL;DR

This paper reviews the tomographic-probability approach in quantum mechanics, discusses entropic uncertainty relations, and introduces a new universal integral inequality based on tomographic entropies.

Contribution

It provides a comprehensive review of quantum state tomography and introduces a novel universal integral inequality derived from entropic uncertainty relations.

Findings

Analysis of optical, symplectic, and spin tomograms of quantum states.

Derivation of a new universal integral inequality for wave functions.

Clarification of the interpretation of quantum tomograms.

Abstract

A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the state tomograms which are considered either as a set of the probability distributions of random variables depending on extra parameters or as a single joint probability distribution of these random variables and random parameters with specific properties of the marginals. Examples of optical tomograms of photon states, symplectic tomograms, and unitary spin tomograms of qudits are given. A new universal integral inequality for generic wave function is obtained on the base of tomographic entropic uncertainty relations.