  We study the relation between energy and entanglement in an entanglement
transfer problem. We first analyze the general setup of two entangled qubits (a
and b) exchanging this entanglement with two other independent qubits (A and
B). Qubit a (b) interacts with qubit A (B) via a spin exchange-like unitary
evolution. A physical realization of this scenario could be the problem of
two-level atoms transferring entanglement to resonant cavities via independent
Jaynes-Cummings interactions. We study the dynamics of entanglement and energy
for the second pair of qubits (tracing out the originally entangled ones) and
show that these quantities are closely related. For example, the allowed
quantum states occupy a restricted area in a phase diagram entanglement vs.
energy. Moreover the curve which bounds this area is exactly the one followed
if both interactions are equal and the entire four qubit system is isolated. We
also consider the case when the target pair of qubits is subjected to losses
and can spontaneously decay.
