Accumulation of entanglement in a continuous variable memory

We study the accumulation of entanglement in a memory device built out of two continuous variable (CV) systems. We address the case of a qubit mediating an indirect joint interaction between the CV systems. We show that, in striking contrast with respect to registers built out of bidimensional Hilbert spaces, entanglement superior to a single ebit can be efficiently accumulated in the memory, even though no entangled resource is used. We study the protocol in an immediately implementable setup, assessing the effects of the main imperfections.