Additivity relations in quantum correlations

TL;DR

This paper investigates how correlations in quantum systems relate through additivity relations, deriving and classifying these relations for total correlation, entanglement, and quantum discord, with implications for understanding quantum correlations.

Contribution

It derives and classifies four additivity relations in quantum correlations from von Neumann entropy's strong subadditivity, linking them to entanglement and quantum discord.

Findings

Four additivity relations in total correlation are derived.

Additive relationships in entanglement are identified.

Quantum discord satisfies similar relations for pure states, not always for mixed states.

Abstract

Does the sum of correlations in subsystems constitute the correlation in the total system? Such a concept can be expressed by an additivity relationship of correlations. From a strong subadditivity condition of von Neumann entropy, four different additivity relations in total correlation are derived and quantified. Based upon the classification of the additivity in total correlation, we identify the corresponding additive relationships in entanglement. It is also discussed that similar relationships are satisfied for quantum discord of pure states, but it is not always true for mixed states.