We study the relationship between the entanglement, mixedness and energy of two-qubit and twomode Gaussian quantum states. We parametrize the set of allowed states of these two fundamentally different physical systems using measures of entanglement, mixedness and energy that allow us to compare and contrast the two systems using a phase diagram. This phase diagram enables one to clearly identify not only the physically allowed states, but the set of states connected under an arbitrary quantum operation. We pay particular attention to the maximally entangled mixed states (MEMS) of each system. Following this we investigate how efficiently one may transfer entanglement from two-mode to two-qubit states.

We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case.

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