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.