Entanglement-Coherence and Discord-Coherence analytical relations for X states

Abstract: In this work we derive analytical relations between Entanglement and Coherence as well as between Discord and Coherence, for Bell-diagonal states and for X states, evolving under the action of several noise channels: Bit Flip, Phase Damping and Depolarizing. We demonstrate that for these families, Coherence is the fundamental correlation, that is: Coherence is necessary for the presence of Entanglement and Discord.