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.Keywords: Quantum Correlations Coherence Entanglement DiscordCorrelations can be found in quantum systems that cannot be classically described; the existence of non-classical correlations in a system is a signature that the subsystems are really quantum. The complete characterization of correlations between parts of a quantum system as well as the interrelations between these correlations is an important subject both from the fundamental and applied point of view. To understand and quantify quantum correlations is of paramount importance to comprehend the origin of the quantum advantages in quantum computing and quantum information processing. Historically, Entanglement was the first quantum correlation known EPR , and over time was the central subject of study, both theoretically and experimentally Horodecki_RMP ; HarocheEPRatoms ; ZeilingerTeleportation . Over time it was understood that there are separable states that show non-classical behavior. Quantum Discord was presented in 2001 Zurek_D , and soon other quantum correlations related to it Modi . Coherence, which is behind the interference phenomenon, has been a main topic in the framework of Quantum Optics. Recently Baumgratz et al. Baumgratz performed a quantitative characterization of Coherence, where quantum coherence is treated as a physical resource. Both Entanglement and Coherence are related to the phenomenon of quantum superposition, therefore it historically was natural to try to understand qualitatively what their relationship is and if there is a quantitative relationship between them XiCoherence ; Adesso_ChE ; Chitambar . That naturally extended to the study of the relation between Coherence and Discord and other related quantum correlations Vedralcoherence ; Fancoherence ; HU20181 . In this work we propounded to study the existence of analytically expressible dynamic relations between Entanglement and Coherence, and between Discord and Coherence, for a simple model such as Bell-diagonal states and for a slightly more complicated one, the X states. In Sec. 2 we do a geometric description of the Bell-diagonal states. In Sec. 3 we present the geometric measures of correlations. In Sec. 4 we find analytical dynamic relations between Entanglement and Coherence and between Discord and Coherence for the Bell-diagonal states evolving under the action of several noise channels: Bit Flip, Phase Damping and Depolarizing. In Sec. 5 we study the X states; we analize their region of existence and its variations with the parameters that describes the X states and calculate the expression of the correlations for these states. In Sec. 6 we study the evolution of the correlations and their dynamical relations under the action of the same channels applied before. In Sec. 7 we discuss Coherence as the fundamental quantum correlation. In Sec. 8 we summarize and discuss the results.2 Geometry of the Bell-diagonal statesThe Bell-diagonal states are a paradigmatic class of states in which, due to their relative mathematical simplicity, it has been possible to study the behavior of various quantum correlations. They can be written as:ρ=14(

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