“…A similar interpretation can be obtained via the state merging protocol [27], Alice (A), Bob (B) and the Environment (E) share a pure tripartite state ρ ABE , she would like to send her state to Bob, keeping the coherence with the system E. They can perform this protocol consuming an amount of entanglement in the process, the amount of entanglement is the regularized quantum discord D ∞ (A : E) ρAE [25,26]. In addition to the above relations, some upper and lower bounds between quantum discord and entanglement of formation have been calculated via the Koashi-Winter relation and the properties of entropy [60][61][62][63]. The Eq.88 was also used to calculate the quantum discord and the entanglement of formation analytically for systems with rank-2 and dimension 2 ⊗ n [41,64,65].…”