Saturation of Coffman–Kundu–Wootters inequalities via quantum homogenization

We study how entanglement between an open system and a reservoir is established. The system is considered to be a qubit, while the reservoir is modelled as a collection of qubits. The system and the reservoir qubits interact via a sequence of partial-swap operations. This processes is called quantum homogenization since at the output the system as well as all reservoir qubits are in states that are, in a limit sense, equal to the original state of the reservoir qubits. We show that in this process the Coffman–Kundu–Wootters inequalities are saturated. This means that no intrinsic multi-partite entanglement is created.