Creation of Two-Particle Entanglement in Open Macroscopic Quantum Systems

We consider an open quantum system of N not directly interacting spins qubits in contact with both local and collective thermal environments. The qubit-environment interactions are energy conserving. We trace out the variables of the thermal environments and N − 2 qubits to obtain the time-dependent reduced density matrix for two arbitrary qubits. We numerically simulate the reduced dynamics and the creation of entanglement concurrence as a function of the parameters of the thermal environments and the number of qubits, N. Our results demonstrate that the two- qubit entanglement generally decreases as N increases. We show analytically that, in the limit N → ∞, no entanglement can be created. This indicates that collective thermal environments cannot create two-qubit entanglement when many qubits are located within a region of the size of the environment coherence length. We discuss possible relevance of our consideration to recent quantum information devices and biosystems.