particular regarding the dimension of the system teleported and the number of parties involved (either as sender, controller, or receiver). d-dimensional systems A generalization to -level systems (so-called qudits) is straight forward and was already discussed in the original paper by Bennett et al.: the maximally entangled state of two qubits has to be replaced by a maximally entangled state of two qudits and the Bell measurement by a measurement defined by a maximally entangled orthonormal basis. All possible such generalizations were discussed by Werner in 2001. The generalization to infinite-dimensional so-called continuous-variable systems was proposed in and led to the first teleportation experiment that worked unconditionally. Multipartite versions The use of multipartite entangled states instead of a bipartite maximally entangled state allows for several new features: either the sender can teleport information to several receivers either sending the same state to all of them (which allows to reduce the amount of entanglement needed for the process) or teleporting multipartite states or sending a single state in such a way that the receiving parties need to cooperate to extract the information. A different way of viewing the latter setting is that some of the parties can control whether the others can teleport. Logic gate teleportation In general, mixed states ρ may be transported, and a linear transformation ω applied during teleportation, thus allowing data processing of quantum information. This is one of the foundational building blocks of quantum information processing. This is demonstrated below. General description A general teleportation scheme can be described as follows. Three quantum systems are involved. System 1 is the (unknown) state ρ to be teleported by Alice. Systems 2 and 3 are in a maximally entangled state ω that are distributed to Alice and Bob, respectively. The total system is then in the state A successful teleportation process is a LOCC quantum channel Φ that satisfies where Tr12 is the partial trace operation with respect systems 1 and 2, and denotes the composition of maps. This describes the channel in the Schrödinger picture. Taking adjoint maps in the Heisenberg picture, the success condition becomes for all observable O on Bob's system. The tensor factor in is while that of is . Further details The proposed channel Φ can be described more explicitly. To begin teleportation, Alice performs a local measurement on the two subsystems (1 and 2) in her possession. Assume the local measurement have