Relation between discrete and continuous teleportation using linear elements

We discuss the relation between discrete und continuous linear teleportation. For this a specific generalization of existing protocols to qudits with a discrete and finite spectrum but with an arbitrary number of states or alternatively to continuous variables is introduced. Correspondingly a generalization of linear operations and detection is made on an abstract level. It is shown that linear teleportation is only possible in a probabilistic sense. An expression for the success probability of this teleportation protocol is derived which is shown to depend only on the relevaut size of the input and ancilla Hilbert spaces. From this rite known results P = 1/2 and P = 1 for the discrete and continuous cases can he recovered. We also discuss the probabilistic teleportation scheme of Knill, Laflame and Milburn and argue that it does not make optimum use of ancilla resources.

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