Hidden correlations and entanglement in single-qudit states

TL;DR

This paper explores hidden correlations and entanglement in single-qudit states, analyzing their informational properties and inequalities using entropic measures, revealing new insights into quantum and classical indivisible systems.

Contribution

It introduces the concept of hidden correlations in single-qudit systems and studies their entropic properties, including analogs of Bayes formula and inequalities for von Neumann and Tsallis entropies.

Findings

Identification of hidden correlations in single-qudit states

Derivation of entropic inequalities for von Neumann and Tsallis entropies

Application of these concepts to qubit and qutrit systems

Abstract

We discuss the notion of hidden correlations in classical and quantum indivisible systems along with such characteristics of the correlations as the mutual information and conditional information corresponding to the entropic subadditivity condition and the entropic strong subadditivity condition. We present an analog of the Bayes formula for systems without subsystems, study entropic inequality for von Neumann entropy and Tsallis entropy of the single-qudit state, and discuss the inequalities for qubit and qutrit states as an example.