Has any work been done on quantum systems which use a combination of types of qunits (eg. using qubits & qutrits simultaneously)?
If work has been done, what kind of work has been done? (eg. in quantum information in general? in quantum computing? in physical implementations?)
Quantum walks are a simple case of quantum dynamics that involves a qubit (named coin in this context) interacting with a high-dimensional qudit (named walker in this context).
Almost anything in quantum optics can be thought of as "combining different qunits" as well: a photon in a superposition of many spatial modes (high-dimensional qudit), together with its polarization degree of freedom (qubit) fits the bill. You can replace "spatial modes" with something like "orbital angular momentum modes" or "frequency modes" or "time modes" and you have the same.
Many quantum algorithms also inherently deal with this scenario: Grover's algorithm and the phase estimation algorithm come to mind (of course, the high-dimensional qudit in those algorithms can be replaced by a number of qubits, but that depends on the context).
Countless other examples could be found, but it would not be very meaningful without specifying the context a bit more.
Yes. Just to give one example, the PPT criterion is necessary and sufficient to decide whether a state is separable for qubit-qubit and qubit-qutrit systems, but not beyond.
