Figure 2

Entanglement differentiation service via Hamiltonian dynamics in a multiuser environment. (a) Protocol 1. Each user gives a different amount of entanglement E(U_i: B_i) ≤ 1 at a global period of time T_π. The differentiation is made in the amount of entanglement (relative entropy of entanglement) by applying the local unitaries for time \({T}_{{U}_{i}}\) for U_i, i = 1, …, K. User U₅ has the highest priority thus the user gets a maximally entangled system, user U₃ is the lowest priority user with and associated with a low amount of entanglement. (b) Protocol 2. All users are assigned with a maximally entangled system, E(U_i: B_i) = 1, and the differentiation is made in the time domain. For users U_i, B_i, i = 1, …, K a particular period of time T_π(U_i: B_i) is assigned, and each local unitary is applied for \({T}_{{U}_{i}}(\pi /{\rm{4}})={T}_{\pi }({U}_{i}:{B}_{i})/{\rm{4}}\) time t o achieve maximally entangled states between the parties. User U₅ has the highest priority thus the user associated with the shortest time period, user U₃ is the lowest priority user with a long time period for the generation of a maximally entangled system.